Question

Verify the identity
cot(theta - pi/2) = -tan theta
I have absolutely no idea on how to do this. Im supposed to be in an algebra 2 class..

Answer 1

i would write cot(theta-pi/2) in terms of cos and sin

Answer 2

then use the cos and sin difference identity

Answer 3

Im completely lost with this problem. I have no idea on the steps or on how to solve it.. Ive been trying to read on how to solev it. But none of it makes sense so far.

Answer 4

do you know how to write cot in terms of cos and sin?

Answer 5

\[\text{ Recall } \cot(u)=\frac{\cos(u)}{\sin(u)} \\ \text{ so } \cot(\theta-\frac{\pi}{2})=\frac{\cos(\theta-\frac{\pi}{2})}{\sin(\theta-\frac{\pi}{2})}\]
now use the difference identities for cos and sin

Answer 6

Its been two years since I was in algrebra. I jsut came out of geometry in sophomore year and now this junior year

Answer 7

Alright one minute. Ill read on it to solve it.

Answer 8

It's a bit easier to understand the origin of the "co-" functions. The "co" comes from "complement:
\[\sin \theta=\cos (\frac{ \pi }{ 2 }-\theta)\]
The TRIG function of an angle is equal to the COTRIG function of the angle's complement.