Science,English,and math 10th

＞＞ The last response from the 9th Science, English, and math

【Look for the trace on creature in the Titan which is the satellite on the Saturn!】

《The probe which flies around the surface on the Titan!》

The area on the dune is called Shangr-la.

After moving varied places so as to investigate, it’ll finally arrive the selk crater, and there is an evidence that a complicated organic matter used to exist and the water of liquid was discovered there.

It is due to research minutely whether or not there is a trace on the chemical reaction which is seen in the first step when a creature was born.

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【Look for the trace on creature in the Titan which is the satellite on the Saturn】

It is planed that the period on the mission is more than two years.

《Approaching the essence on the life from Titan》

It has been thought the air made from nitrogen and methane resembles the one in the primitive earth, so if being able to know what kind of chemical reaction was done in that environment, it is a clue to know what kind of chemical reaction was done on the earth before.

On the other hand, the sea of Titan is made from the liquid of methane, therefore as to the structure on the cell must have…

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【Look for the trace on creature in the Titan which is the satellite on the Saturn!】

《Approaching the essence on the life from Titan》

…therefore as to the structure on the cell must have been different from the the one on the earth, even if the life was born there.

If the life which was born altogether different from the environment on the earth had something common with the life on the earth, it will be a great hint against a question, what is the essential to the life? As a result, looking for the trace on the creature with the Titan is very significant, the specialist said like that.

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【Hayabusa Ⅱ succeeded in touching down second times】

《It succeeded in taking the material underground on the steroid for the first time in the world》

Hayabusa Ⅱ which is the probe in JAXA succeeded in touching down on the steroid called Ryugu second times for the first time in the world July in 2019. It could take material from both on the surface and the underground.

Analyzing the material which was taken may have approached the mystery on the solar system or on the origin on life.

JAXA is an abbreviation on Japan Aerospace Exploration Agency. The manager who was engaged in the mission…

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【Hayabusa succeeded in touching down twice】

《It succeeded in taking material underground on the steroid for the first time in the world》

The manager who was engaged in the mission said he was relieved that the last big mission for him succeeded in going well.

《Making an artificial crater and taking fresh material from underground》

It has been thought as to planets in the solar system, including the earth, numberless little celestial bodies collide, united and formed. The one who survived from the celestial body and has been thought maintaining the situation when the solar system formed.

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【Hayabusa succeeded in touching down twice】

《Making an artificial crater and taking fresh substance from underground》

Steroids which are more than eight hundred thousand have been discovered at present, and one of them is Ryugu. Ryugu is the one of which type is C, including lots of organic matter which is raw material from the life.

If being able to find the organic matter from the Ryugu, it will be a significant clue so as to know the origin on the life on the earth. Taking material by the Ryugu was raised as target in the project by the Hayabusa second.

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【Hayabusa succeeded in touching down twice】

《Making a artificial crater and taking fresh material from underground》

It was planned to touch down twice in total, and taking the material from the surface in the first time, and doing from underground in the second.

It is high possible that the material on the surface receives weathering in the universe. The weathering in the universe is the action changing by receiving collision with meteorite, radiation, heat and light from the sun.

So taking advantage of device for collision was used and driving mass of copper into the ground, and making…

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【Hayabusa succeeded in touching down twice】

《Making an artificial crater and taking fresh material from the underground》

…and making an artificial crater, making the material underground expose and setting up the situation which resembles the time when the solar system was formed.

Hayabusa Ⅱ succeeded in taking the material from the surface, and making the artificial crater of which diameter is some 10 meter went well February in 1922, and taking the fresh material from underground by making the artificial crater was about to do in the first time in the world.

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【Hayabusa succeeded in touching down twice】

《Touching down was done outside the crater. Why?》

Actually it was assumed to touch down inside the artificial crater , or near place from the crater from the first time.

When researching the artificial crater actually, its tilt was harder than it was assumed, and it proved touching down inside the artificial crater was dangerous, but the manager who was engaged in the touching down said he didn’t always stick to touching down and said like the next.

When making the artificial crater, the material scattered inside the crater from the underground.

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【Hayabusa Ⅱ succeeded in touching down twice】

《Touching down was done outside the artificial crater. Why?》

If touching down at the place where the material from the underground scattered, adopting the material from the underground is done easily. Furthermore, he said on the strong point on touching down outside the crater like the next.

The material on the surface and the other from the underground was mixed outside the crater, so when touching down once there, taking both of the material with a single action alone and it’s all right.

Not only researching difference between the …

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【Hayabusa Ⅱ has succeeded in touching down twice】

《Touching down was done outside the artificial crater. Why?》

Not only being able to research difference between the material on the surface and that on the underground, but comparing it with the one which was adopted in the first touch down, so it is possible to research the difference between the material on the surface from different places.

When researching the outside the artificial crater by using an optical camera attached to the Hayabusa Ⅱ, it was verified it was discovered a place where the material on the underground fell and piled.

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【Hayabusa Ⅱ succeeded in touching down twice】

《Touching down was done outside the artificial crater. Why?》

The result on the research of the place where the material on the underground was piled in detail, there was none of tremendous rock there, so the Hayabusa Ⅱ fell a marker there as target for touch down.

The one who was engaged in the mission said touching down was very dangerous. The touching down went well and the material on the surface was adopted then, so it was hard to judge whether or not it was done the second time.

《Obtaining a fragment on the history in the solar system》

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【Hayabusa Ⅱ succeeded in touching down twice】

《Obtaining a fragment on the history in the solar system》

Hayabusa Ⅱ started to descend from the height of twenty thousand kilometers. When reaching the height of five hundred meters, final check on the Hayabusa Ⅱ was done, and the leader on the mission showed to go ahead, after that Hayabusa Ⅱ touched down for itself.

Rising the body on Hayabusa Ⅱ which seemed to after the touch down was confirmed in the control room, and big applause occurred there then, and the leader said they won the fragment on the history of the solar system happily.

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【Hayabusa Ⅱ succeeded in touching down twice】

《Obtaining a fragment on the history in the solar system》

Hayabusa Ⅰ is the predecessor on the Ⅱ, and the lots of troubles like fuel leakage, being unable to communicating with the earth occurred to the predecessor, but the leader said there wasn’t any of big trouble in the Hayabusa Ⅱ. The apparatus on the probe functioned normally, and the touch down went well, for we could utilize the past experience on the predecessor.

《Looking forward to returning Hayabusa Ⅱ》

Hayabusa Ⅱ planed to depart from the asteroid called Ryugu at the end of 2019.

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【Hayabusa Ⅱ succeeded in touching down twice】

《Looking forward to returning Hayabusa Ⅱ》

Ryugu is the asteroid of which diameter is some nine hundred meters, and revolves around the sun in 1.3 years.

Hayabusa Ⅱ planned to approach the earth at the end of 2020, and to separate its capsule toward the earth, then the capsule would storm into the atmosphere at the speed of 12 kilometers per hour, and the temperature on the surface would reach no less than three thousand degrees.

Hayabusa Ⅱ adopted the material on the surface of the ground in the first time, and the mixture of the surface on…

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【Hayabusa succeeded in touching down twice】

《Looking forward to returning Hayabusa Ⅱ》

…and at the second time, Hayabusa Ⅱ obtained the mixture the material on the surface of the ground and that from the underground. Adopting the material from the two place of which depth is different is the first brilliant achievement in the world.

Hayabusa Ⅰ brought back with a sample from other asteroid called Itokawa, and its size was no more than 0.3 millimeters at best and most of them were particulate matters of which size was dozens of micro meters.

1 micro meter is thousandth of 1 millimeter.

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【Hayabusa succeeded in touching down twice】

《Looking forward to returning Hayabusa Ⅱ》

On the other hand, the sample from the asteroid called Ryugu is expected to be the particulate matters of which size is a few millimeters. The researchers said they thought they could understand various things with a standpoint of the structure on the rock and sand.

Then researchers could receive various knowledge by analyzing the particulate particles on the history of the formation on the solar system, but Ryugu is the asteroid of which nature is different from Itokawa, so it’s expected lots of organic…

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【Hayabusa succeeded in touching down twice】

《Looking forward to returning Hayabusa from the asteroid》

…so it’s expected to exist lots of organic matters which were raw material for a life.

The point on analysis this time is water and organic matter, and when comparing the material on the Ryugu with that on Itokawa, there would be still more new discoveries, the leader on the mission of touching down Hayabusa said like that.

【Simple and useful. Trigonometric function from the scratch】

Sin, cosine, and tangent. These are trigonometric function which we learn at high school.

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【Simple and useful. Trigonometric function from the scratch】

The trigonometric function is the function which expresses the relation between angle and length on a right triangle.

There are lots of people who may have thought they never make use of the trigonometric function in actual life, but it isn’t exaggerated without the trigonometric function, the modern society isn’t supported.

When did the trigonometric function start to use? Its origin dates back to B.C. The human being has made use of the nature on the trigonometric function and developed surveying, astronomy, and science.

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＞＞19

I’m going to comment on the trigonometric function which is indispensable existence for the human being from the base to application, the author said like that.

I’m going to my best.

【The nature on the triangle】

《Triangle is the base for all the figures. What is the significant nature in which the triangle has?》

The trigonometric function is the function on triangle. The author said he was going to express the interesting nature on the triangle before expressing the trigonometric function in detail.

The triangle is the basic for all the figures. Why?

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【The nature on triangle】

《The triangle is the base for all the figures. What is the significant nature in which the triangle has?》

Because polygons like a square or pentagon is divided into some triangles. There is no exceptions. To put it the other way around, if combined into some triangles, we can make any complicated figure. Its nature has been taken advantage of in video game, computer graphic, or Japanese cartoon. In general, gathering triangle together is called polygon.

《There is a substantial building owing to the triangle?》

When making a construction, the triangle is useful.

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【The nature on triangle】

《There is a substantial building due to a triangle?》

The framework of which base is the triangle is called Truss structure, and is used for an iron bridge.

As to the triangle, if the length on three sides are fixed, the positions on three vortexes and angles are fixed automatically, but other polygons like a square doesn’t go well like that.

If adding all the interior triangles in a triangle, it’s always 180 degrees. If knowing it, when being able to know two angles in the triangle, we can find the other angle with a calculation.

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【Pythagorean theorem】

《Pythagorean theorem which is true under right triangle. When knowing it, what is useful for it?》

Trigonometric function is the one on the sides and angles of right triangles. There is a significant nature in the right triangle which is known as the Pythagorean theorem.

There is a right triangle, its side is a, b, and c, and the c is the longest hypotenuse 斜辺, and there are three squares of which each side is a, b, and c. The area of the square on the c is equal to the addition of the area on the b and a. It’s the Pythagorean theorem.

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【Pythagorean theorem】

To put it other way around, a triangle which is true under the Pythagorean theorem, it’s always the right triangle.

《How far can we see from the Sky Tree in Japan?》

The sky tree of which height is 634 meters in Tokyo. How far can we see from there? If using the Pythagorean theorem, we can calculate its distance.

When drawing a tangent 接線 from the tip of the sky tree to the cross section of the earth which is the circle, the contact place where the tangent and the circle meet up with the farthest place from the sky tree where we can see.

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【Pythagorean theorem】

《How far can we see from the sky tree in Japan?》

The line which connects the center on a circle with the tangent has nature of going straight, so if connecting the center of the circle, the tip of the sky tree, and the contact point, it appears a right triangle.

We know the radius on the earth and the height on the sky tree, so if using the Pythagorean theorem, we can calculate the distance which we seek is some ninety kilometers.

【Triangulation】

《Making use of the nature on triangle, the accurate map was made》

The triangulation is triangular surveying.

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【Triangulation】

《Taking advantage of the nature on triangle, the accurate map was made》

There is a trigonometric point in a place with a fine view where we can see from far away like the summit on a big mountain. It’s the basic point for the triangulation of making a precise map.

Measuring two far away place like Aomori prefecture and Kagoshima prefecture is hard actually, but if making use of the triangulation, we can do it.

As to the triangle, when the length on a side and the two angles on the both side are fixed, its size and shape are also determined. The triangle has nature like that

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【Triangulation】

The triangulation is the one which we make use of the nature on the triangle.

《It’s the first basic line which we survey actually》

The author said he was going to show the procedure on the triangulation concretely.

At first, setting the two triangulation which are the base and connects two of them. It’s the basic line, and measuring the basic line as accurate as possible.

In the next, setting the place where we can see from the two of triangulation is the third triangulation, and measuring angles on the both end of the basic line. There is the first triangle.

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【Triangulation】

《It’s the first basic line which we measure actually》

In the next, setting the fourth triangulation on the opposite direction and measure the angle on the both end. It’s the second triangle.

When drawing the two triangle with a setting reduced scale on the paper, we can write down accurate relation on the place of the four triangulation.

Besides, connecting the third and fourth triangulation and it’s the new basic line and making bigger triangles and drawing them on the paper. If repeating it, and we have only to measure the angle, as the first basic line as the base.

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【Triangulation】

《It’s just the first basic line which we measure actually》

If repeating it, we can make the precise map which is wide range as we like as principle.

As to the distance to the new triangle, without measuring actually, we can seek from the length on the basic line and its angle by using the theorem on the trigonometric function which the author said he was going to show later. It’s the strong point on the triangulation, the author said like that.

【Origin on the trigonometric function】

《An astronomer in the Ancient Greece made use of the triangulation for the astronomy》

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【Origin on the trigonometric function】

《An astronomer in the Ancient Greece took advantage of the triangulation for astronomy》

If using a ruler, we can survey the length on the side of a triangle, but if it’s too big, it’s hard to do it actually.

On the other hand, as to its angle, even if the triangle becomes very huge, we can measure it comparatively easy, and the people in the ancient age were already aware of it from earlier time, and the trigonometry was completed then.

Making use of the relation between the length on the side and the angle in a triangle and surveying long distance.

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【Origin on the trigonometric function】

《An astronomer in the Ancient Greece made use of the triangulation for astronomer》

The triangulation is the way of knowing the long distance which we can’t measure actually.

In the ancient time, when using the triangulation, making the list on the numerical value so as to seek the distance from the angle, and taking advantage of the list and sought the distance.

The one is Hipparchus who changed the list on the numerical value into a book for the first time. He was an astronomer in the Ancient Greece in the B.C. Second century.

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【Origin on the trigonometric function】

《The list on the chord made by Ptolemy develops into the trigonometric function》

It’s other astronomer,Ptolemy who developed the list on the numerical value made by Hipparchus. He spoke the Ptolemaic theory 天動説 in his book and put on the list of the numerical value in his book. The list is called the one on the chord.

The list made by Hipparchus was changed into more precisely by Ptolemy. Astronomers in the ancient time made full use of the triangulation and the list on the chord and observed an angle, and calculated accurate position on the celestial…

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【Origin on the trigonometric function】

《The list on the chord made by Ptolemy develops into the trigonometric function》

…and calculated precise position on the celestial bodies in the celestial sphere from the angle. The celestial sphere is the sphere which fixed stars except for the sun were clung to. The ancient people thought like that.

The list on the chord was conveyed to Persia and India and changed into the better and more useful one, and its outcome was transferred to Europe in the Middle Ages.

After that mathematicians improved it into more accurate one and the trigonometric…

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【Origin on the trigonometric function】

…and the trigonometric function is completed.

Hipparchus is the astronomer who classified the stars in the night sky into from the first−magnitude to the sixth−magnitude and put together catalog on the fixed stars which reached number of 850. Any book written by Hipparchus doesn’t exist at present, but his outcome on the study was put together in the book written by Ptolemy.

【The trigonometric function is so simple!】

The trigonometric function which we learn in high school is three kinds, sine, cosine, and tangent.

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What kinds of feature on the three sorts of the trigonometric function? What kind of situation are they useful?

【What is the sine?】

《Let’s measure the numerical value on the sine with a ruler and compass》

The first trigonometric function is the sine, and the word on the sine is the one which is expressed in English. Sin is the one which is used on math.

Pi is the constant number of which numerical value is 3.14…it’s a fixed numerical value, on the other hand, there isn’t any fixed numerical value in the sine.

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【What is the sine?】

《Let’s measure the numerical value on the sine with a ruler and a pair of compasses》

When given an angle, the numerical value on the sine is fixed, and something of other numerical value for the former one is called the function in math.

Please look at the triangle on the lower part of the illustration. It’s a Greek letter for the angle of θ, and the numerical value on sin θ is expressed as sin θ, and it’s defined the value of dividing the height on the right triangle by the hypotenuse 斜辺.

If the length on the hypotenuse is 1, the height is the value on the sin θ.

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【What’s the sine?】

Besides, if sin θ multiplying by the hypotenuse, the height is sought.

《What is the value for sine 30 degrees?》

The author said he was going to measure the numerical value on the 30 degrees. Making the point A which is right next to the compass rotate with 30 degrees to anti-clockwise like drawing a circle of which radius is 10 centimeters.

The point which is right next to the compass is the starting point on the rotation. Then measuring the height on the B which is ahead of the tip of the pencil, and the height must have been just 5 centimeters.

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＞＞36

【What’s the sine?】

《What is the numerical value on the sin 30 degrees?》

The height divided by the length on the radius is the numerical value on the sin 30 degrees. It’s 0.5. It’s expressed like sine 30 degrees is equal to 0.5.

As to the sine which is defined in the right triangle, we can handle from 0 to 90 degrees alone, but if thinking with the rotation like that, we can deal with any kind of angle. If the point
B is under the center, the sin is defined θ as negative number.

Thus the one which is defined by the rotation is the trigonometric function.

【The way of using the sine】

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【The way of using the sine】

《If being aware of the numerical value on the sine, we can install a solar panel wisely》

What is the situation in which the sine is useful? For instance, when installing a solar panel, the value on the sine is useful. When installing, it is done with an angle which can receive the sunlight as directly as possible, it’s ideal position.

In general, the larger the latitude is, the bigger the angle on which the sunlight shines is , and the less the latitude is, the less the angle is.

As a result, the angle that installing the solar panel is inclined is fixed…

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＞＞39

【The way of using the sine】

《If being aware of the numerical value on the sine, we can install the solar panel wisely》

…the angle that installing the solar panel is fixed according to the latitude on the area where the solar panel is installed.

In Tokyo prefecture, it is said that directing the solar panel to south and installing with the angle of 30 degrees from the ground is ideal.

《What should we do if wanting to install the solar panel of which vertical width is 1 meter with 30 degrees from the ground?》

If installing the solar panel of which vertical width is 1 meter with 30…

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＞＞39

【The way of using the sine】

《What should we do if wanting to install the solar panel of which vertical width is 1 meter with 30 degrees from the ground?》

If installing the solar panel of which vertical width is 1 meter with 30 degrees from the ground, what is the height on the vertical post at the top of the back of the solar panel?
This is the time when we make use of the value on the sine. The numerical value for the sin 30 is 0.5.

In short, if the vertical width on the solar panel is 1 meter, it’s just that we have only to multiplying 1by 0.5, so if preparing the post of which…

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＞＞39

【The way of using the sine】

《What should we do if wanting to install the solar panel of which vertical width is 1 meter with 30 degrees from the ground?》

…so if preparing for the post of which length is 0.5 meter of multiplying 1 by 0.5, we must have installed it with the inclination on 30 degrees.


Furthermore, we can know the numerical value on the sin θ for the angle of θ with scientific electronic calculator or with the trigonometric function table.

【What is the cosine?】

《Let’s measure the numerical value on the cosine with a ruler and a pair of compasses》

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【What is the cosine?】

《Let’s measure the numerical value on the cosine with a ruler and a pair of compasses》

The second trigonometric function is cosine. The cosine means 余弦 in English, and is expressed cos in math. When being given an angle, the numerical value on the cosine is fixed like the sine.

The numerical value on the cosine for the angle of θ in the right triangle on the lower part in the illustration is expressed cos θ, and is defined as the numerical value that the length on the base divided by the length on the hypotenuse.

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＞＞43

【What is the cosine?】

《Let’s measure the numerical value on the cosine with a ruler and a pair of compasses》

When the length on the hypotenuse is 1, the length on the base is the numerical value on the cos θ, and if the length on the hypotenuse multiplying by the cos θ, it’s the length on the base.

As you know, I’ve expressed myself in English, based on the book of Newton at present, but whether or not the length on the hypotenuse is 1, the length on the base is the numerical value on the cos θ, I’m wondering.

《What is the numerical value on the cos 30 degrees》

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＞＞43

【What is the cosine?】

《What is the numerical value on the cosine for 30 degrees?》

The author said he was going to measure the numerical value on the cosine for 30 degrees like the sine.

Making the point A which is next to the compass rotate counter clockwise with 30 degrees like drawing a circle of which radius is 10 centimeters in the illustration. The A is the starting point for the rotation.

Then we measure the distance between the point of B which is ahead of the tip of the pencil and the center on the circle. Its length could have been some 8.7 centimeters, and divided it by…

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＞＞43

【What is the cosine?】

《What is the numerical value on the cosine for 30 degrees?》

…and divided the distance between the B and the center on the circle by the length on the radius is some 0.87, and it’s the numerical value on the cosine for 30 degrees.

Its equation is expressed in the illustration in the thread of No.43, but the equation adopts the fraction and root, I should have expressed either or in English or in mathematical expression, but I don’t know how to express the mathematical expression here, using the fraction, so I’m going to omit it. I’m sorry for it.

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＞＞43

【What is the cosine?】

Without adopting the right triangle, if using the rotation like that, even if the θ is any kind of angle, we can define the cos θ.

【The way of using the cosine】

《Tadataka Ino who made full use of the numerical value on the cosine so as to make a precise map》

Without GPS and no one knew the triangulation in the Edo era, but Tadataka Ino made a Japanese map which is extremely accurate then. The one which supported his feat was the triangulation like the cosine.

He walked all over Japan for himself, and repeating measuring the distance between two points patiently

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【The way of using cosine】

As to measuring the distance, without converting from the number of steps, using a string or chain and measured it exactly.

《The list on the trigonometric function which Tadataka Ino brought with himself》

The place where Tadataka Ino adopted the cosine was the one where there was a tilt and he measured the distance there. He always carried a list which was equivalent to the one of the numerical value on the sine, cosine, and tangent at present.

The distance between the two places where there was the tilt is equivalent to the hypotenuse in the right triangle.

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【The way of using cosine】

《The list on the trigonometric function which Tadataka Ino carried with himself》

He measured the angle of inclination with his tool called 象限儀 and looked up the numerical value on the cosine according to the angle with the list, and multiplying it by the length on the hypotenuse, and could seek the distance on the map. The length on the hypotenuse multiplying by cos θ is the horizontal distance.

Tadataka Ino started to learn astronomy and land surveying at the age of fifty, and travelled all over Japan for surveying at the age of fifty five.

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＞＞49

It is said that his map was so accurate that foreigners who visited Japan so as to measure were surprised at the precision on the map.

【What is tangent?】

《Let’s measure tangent with a ruler and a pair of compasses》

The third trigonometric function is tangent. The tangent means 接線 or 正接 in Japanese. It’s expressed tan in math. When being given an angle, the numerical value on tangent is fixed like the sine and cosine.

The numerical value on tangent is expressed tan θ, and is defined as the one which divided the height on the right triangle by the length on the base.

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