Question

What is `cos(pi/2 - theta)` in simplest form?

Answer 1

`cos(pi/2 - theta) = sin(theta)`

Explanation:

`cos(pi/2 - theta) = sin(theta)`

This is most easily seen when `0 < theta < pi/2`:

Consider a right angled triangle with angles `theta`, `pi/2 - theta` and `pi/2`.

Then calling the side cloest to the angle `theta` the "adjacent" side, note that this is "opposite" for the angle `pi/2 - theta`.

So we have:

`sin theta = cos (pi/2 - theta) = "opposite"/"hypotenuse"`

`cos theta = sin (pi/2 - theta) = "adjacent"/"hypotenuse"`

Answer 2

`sin theta`

Explanation:

Here's an example:

You know that `cos theta = b/c`.

So if you took `cos(pi/2-theta)`, it'd be cosine of angle B (not labeled above), which is equal to `a/c`. Notice that `sin theta` also equals `a/c`. Thus, `cos(pi/2-theta) = sin theta`.