Question

Question #f154e

Answer 1

`x = 450° or 630°`

Explanation:

`-2cos(x/3) = sqrt(3)`
`cos(x/3) = -(sqrt(3)/2)`
`cos(30) = sqrt3/2`
cosine is negative in 2^(nd) and 3^(rd) quadrants.
`:. (x/3) = (180-30)° or (180+30)°`
`x = (150*3)° or (210*3)°`
`x = 450° or 630°`

Answer 2

`x = +- (5pi)/2 + 6kpi`

Explanation:

`- 2cos (x/3) - sqrt3 = 0`
`cos (x/3) = - sqrt3/2`
Trig Table and unit circle give 2 solutions:
`x/3 = +- (5pi)6 + 2kpi`
`x = +- (15pi)/6 + 6kpi = +- (5pi)/2 + 6kpi =`