Question

Are there any anglesθsuch that sin(θ) = cosθ? If yes, then determine all such anglesθ. If not, thenexplain why not.

Answer 1

The answer is `theta in {pi/4+kpi}`, `AA k in ZZ`

Explanation:

`sintheta=costheta`

Therefore,

`sintheta/costheta=1`

`tantheta=1`

`theta=pi/4+kpi`, `AA k in ZZ`

If you plot `sintheta` and `costheta`, you will see the points of intersection.

graph{(y-sinx)(y-cosx)=0 [-3.96, 16.04, -4.32, 5.68]}