"Why is cosθ=sin(90-θ)? Use the figure to help explain."
I attached the image.
In this instance, I am at a complete loss...
Drop a perpendicular from the point (u,v) down to the u axis, and another perpendicular from (u,v) horizontally over to the v axis. Label the line from the origin to (u,v) - call it h. Now, you tell me: from the definitions, what is the cosine of theta? What is the sin of (90 - theta)?
One acute angle is and the other is since the acute angles sum to 90 degrees in a right-angled triangle.
Place at the acute angle coming away from the base.
Label that side at "base"
Then as the base is adjacent
as the base is opposite the angle