why is sin(90-θ) = cosθ?

Question

why is sin(90-θ) = cosθ?

In: 0

Answer 1

Because the angles of all triangles sum to 180 degrees.

So, in a right triangle, the two non-right angles must sum to 90 degrees (because the right angle itself is 90 degrees).

So if one of those angles is theta, the other angle must be 90-theta (in degrees).

And, in a right triangle, the side opposite one angle is adjacent to the other.

So the side adjacent to the theta angle is opposite to the 90-theta angle.

And the lengths of those sides each divided by the length of the hypotenuse will give you the cosine of theta and the sin of 90-theta, by definition of those functions.