Thread: Stumped... cosθ=sin(90-θ)

"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)?

Make right triangles from the point (u,v) and use the definitions of sine and cosine. Or use a unit circle for another geometric proof.
But it's simpler to use the sine Difference Formula!

Originally Posted by wiseguy

"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...

??

For simplicity, if you draw a single right-angled triangle.

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