Question

HELP
Question: Determine all values where sin x = cos x for -360 ≤ x ≤ 360

Answer 1

One way to do this would be to recognize that sin x / cos x = tan x.

So, if you begin with sin x + cos x = 0 and divide all 3 terms by cos x, you get

sin x
----- = tan x + 1 = 0, or tan x = -1. Can you solve that for x? You might want
cos x

to graph tan x between -360 and +360 degrees. Where does the tangent have the value -1?

Answer 2

I like a transformation that seems to be mostly forgotten.

\(\sin(x) - \cos(x) = \sqrt{2}\cdot \sin\left(x - \dfrac{\pi}{4}\right)\)

Answer 3

Rfb34: Please, if you post a question, stick around for a while to see whether someone responds offering to be of help. As a rule, I don't invest much, if any, time in helping those who are not online.