Question

How do you solve `sinx+cosx=0`?

Answer 1

`(3pi)/4; (7pi)/4`

Explanation:

Use trig identity.
`sin x + cos x = sqrt2cos (x - pi/4) = 0`
`cos (x - pi/4) = 0`
Unit circle gives 2 solutions:
a. `x - pi/4 = pi/2`
`x = pi/2 + pi/4 = (3pi)/4 + 2kpi`
b. `x - pi/4 = (3pi)/2`
`x = (3pi)/2 + pi/4 = (7pi)/4 + 2kpi`