Question

Question #f2a52

Answer 1

`x = pi/4 + kpi`
`x = (3pi)/4 + kpi`
`x = +- (2pi)/3 + 2kpi`

Explanation:

cos 2x(2cos x + 1) = 0
Either term must be zero.
a. cos 2x = 0. Unit circle gives 2 solution:
`2x = pi/2 + 2kpi`, and `2x = (3pi)/2 + 2kpi`.
`2x = pi/2 + 2kpi` --> `x = pi/4 + kpi`
`2x = (3pi)/2 + 2kpi` --> `x = (3pi)/4+ kpi`
b. 2cos x + 1 = 0
`cos x = - 1/2`
Trig table and unit circle gives -->
`cos x = - 1/2` --> `x = +- 2pi/3 + 2kpi`
General answers:
`x = pi/4 + kpi`
`x = (3pi)/4 + kpi`
`x = +- (2pi)/3 + 2kpi`