How do you calculate (co-)sine values ​​in the unit circle?

The question occurred to me as I am currently working on this task:

I don't know what to do to solve the problem.

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Rammstein53
1 year ago

An angle of 20 degrees is shown in the following image.

a = cos(20°), b = sin(20°), c = 1 (radus from the unit circle)

Because of cos(0°)=+1, cos(20°) is somewhat smaller than +1. The value 0.9 fits best. The cosine reaches a value of +0.5 only at an angle of 60 degrees.

The same applies to the sine. Because of sin(0°)=0, sin(20°) is somewhat larger than 0. The value 0.3 fits best.

In addition, the triangle ABC is rectangular, so it applies

a2 + b2 = c2 = 1

and

cos2(x) + sin2(x) = 1

This can also help to approximately determine the values of sine and cosine.

Halbrecht
1 year ago

about 20°

slanted length is 1 , the hypotenuse
Senkrecht: Countercathete for sine
Waagrecht : Ankathete for Cosinus