Question

How do you solve `sec((3x)/2)+2=0` and find all general solutions?

Answer 1

`+- (4pi)/3 + (4kpi)/3`

Explanation:

`sec ((3x)/2) = - 2`
`1/cos((3x)/2) = - 2`
`- 2cos ((3x)/2) = 1`
`cos ((3x)/2) = - 1/2`
Trig table and unit circle give as solution arcs:
`(3x)/2 = +- (2pi)/3 + 2kpi`
`3x = +- (4pi)/3 + 4kpi`
`x = +- (4pi)/3 + (4kpi)/3`