Question

How do you solve `4secx+8=0`?

Answer 1

`x=120^@=(2pi)/3`

Explanation:

`4secx+8=0`
or
`4secx=-8`
or
`secx=-8/4`
or
`secx=-2`
or
`1/cosx=-2`
or
`cosx=-1/2`
or
`cosx=cos120^@`
or
`x=120^@=(2pi)/3`

Answer 2

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

Explanation:

`sex x = 1/(cos x) = -8/4`
`cos x = -4/8 = - 1/2`
Trig table of special arcs, and trig unit circle -->
`cos x = - 1/2` --> arc `x = +- (2pi)/3`
The arc `-(2pi)/3` is the same as the arc `(4pi)/3` --> co-terminal arcs.
General answers:
`x = (2pi)/3 + 2kpi`
`x = (4pi)/3 + 2kpi`