Question

Question #38271

Answer 1

`pi/4`

Explanation:

sin x - cos x = 0
Use trig identity:
`sin x - cos x = sqrt2sin (x - pi/4)`
`sqrt2sin (x - pi/4) = 0`
`sin (x - pi/4) = 0`
Unit circle gives 3 solutions:
a. `(x - pi/4) = 0` --> `x = pi/4`
b. `x - pi/4 = pi`--> `x = pi + pi/4 = (5pi)/4` (out of interval)
c. `x - pi /4 = 2pi` --> `x = 2pi + pi/4 = (9pi)/4 = pi/4`