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Lösung 4.2:3c

Aus Online Mathematik Brückenkurs 1

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For example, if we can subtract sufficiently many <math>2\pi</math>'s from <math>9\pi</math>, we will obtain a more manageable argument which lies between <math>0</math> and <math>2\pi\,</math>,
For example, if we can subtract sufficiently many <math>2\pi</math>'s from <math>9\pi</math>, we will obtain a more manageable argument which lies between <math>0</math> and <math>2\pi\,</math>,
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{{Displayed math||<math>\sin 9\pi = \sin (9\pi - 2\pi - 2\pi - 2\pi - 2\pi) = \sin \pi\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>\sin 9\pi = \sin (9\pi - 2\pi - 2\pi - 2\pi - 2\pi) = \sin \pi\,\textrm{.}</math>}}
The line which makes an angle <math>\pi</math> with the positive part of the ''x''-axis is the negative part of the ''x''-axis and it cuts the unit circle at the point (-1,0), which is why we can see from the ''y''-coordinate that <math>\sin 9\pi = \sin \pi = 0\,</math>.
The line which makes an angle <math>\pi</math> with the positive part of the ''x''-axis is the negative part of the ''x''-axis and it cuts the unit circle at the point (-1,0), which is why we can see from the ''y''-coordinate that <math>\sin 9\pi = \sin \pi = 0\,</math>.
[[Image:4_2_3_c.gif|center]]
[[Image:4_2_3_c.gif|center]]

Version vom 08:51, 22. Okt. 2008

We can add and subtract multiples of 2 to or from the argument of the sine function without changing its value. The angle 2 corresponds to a whole turn in a unit circle and the sine function returns to the same value every time the angle changes by a complete revolution.

For example, if we can subtract sufficiently many 2's from 9, we will obtain a more manageable argument which lies between 0 and 2,

sin9=sin(9−2−2−2−2)=sin.

The line which makes an angle with the positive part of the x-axis is the negative part of the x-axis and it cuts the unit circle at the point (-1,0), which is why we can see from the y-coordinate that sin9=sin=0.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_4.2:3c“