Question

Question #23b7a

Answer 1

`theta = pi/30 + (2pi)/5 * n , (11pi)/30 + (2pi)/5 * n`, `n=0,1,2,3,...`

Explanation:

`cos 5theta = sqrt3/2`

`5theta = cos^(-1)(sqrt3/2)`

`5theta = 1/6 pi, 11/6 pi, 13/6 pi, 23/6 pi, 25/6 pi, 35/6 pi...`

`theta = 1/30 pi, 11/30 pi, 13/30 pi, 23/30 pi, 25/30 pi, 35/30 pi...`

we can divide into 2 type of sequences.
`theta = 1/30 pi, 13/30 pi, 25/30 pi,...` `->i`
`theta = 1/30 pi, 1/30 pi + 12/30 pi, 1/30 pi + 24/30 pi,...`
`theta = 1/30 pi + 12/30 n * pi`

`theta = 1/30 pi + 2/5 n * pi`, `n=0,1,2,3,...`

`theta = pi/30 + (2pi)/5 * n`, `n=0,1,2,3,...`

`theta = 11/30 pi, 23/30 pi, 35/30 pi,...` `->ii`
`theta = 11/30 pi, 11/30 pi + 12/30 pi, 11/30 pi + 24/30 pi,...`
`theta = 11/30 pi + 12/30 n * pi`,

`theta = 11/30 pi + 2/5 n * pi`, `n=0,1,2,3,...`

`theta = (11pi)/30 + (2pi)/5 * n`, `n=0,1,2,3,...`

Answer 2

`t = +- pi/30 + (2kpi)/5`

Explanation:

`cos 5t = sqrt3/2`
Use trig table and unit circle:
`5t = +- pi/6 + 2kpi`
General answer:
`t = +- pi/30 + (2kpi)/5`
If you don't want a negative arc answer, you may replace the arc
`(-pi/30)` by the co-terminal arc `(59pi)/30`.
General answer:
`t = pi/30 + (2kpi)/5`
`t = (59pi)/30 + (2kpi)/5`