Wednesday, February 09, 2011

At me of 720 degrees how further to find a sine and cosine of corner?

"And what if at a finding of value of corner equal 4pi, at me of 720 degrees how further to find a sine and cosine of corner??" - such question has been set in comments. Really, how to find trigonometrical function if a corner the alpha is more than 360 degrees?

Present that all corners 360 degrees there are more or 2 pi is a ball of a yarn. To learn values of trigonometrical functions for such corners, this ball of a yarn needs to be unwound at first. One coil of a yarn equals to a corner in 360 degrees or 2 pi. To unwind a ball it is necessary until value of a corner does not become less than 360 degrees or 2 pi. After that under the table of values of trigonometrical functions or on a trigonometrical circle we find value of the necessary trigonometrical function.

720° - 2 x 360° = 0°

The same focus with corners in radians will look so:

4π - 2 x 2π = 0

For a corner of 720 degrees or 4 pi it turns out that a sine and cosine same, as well as for a corner of 0 degrees. The decision can be written down so:

sin 720° = sin 4π = sin 0 = 0

cos 720° = cos 4π = cos 0 = 1

The sine of 720 degrees or 4 pi is equal to a sine of zero of degrees and is equal to zero. Cosine 720 degrees or 4 pi it is equal cosine zero of degrees and it is equal to unit.

What for all these troubles with such big corners are necessary? I have knowingly mentioned a yarn ball. Let's try together it not only to untangle, but also we will look, as it is reeled up and what for in general is necessary.

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