Question

How do you find the solution to `2-sectheta=5+sectheta` if `0<=theta<360`?

Answer 1

`theta = 131.8`

Explanation:

rearranging the terms we get
`-2sectheta = 3` or `2sectheta = -3`

`sectheta = -3/2`

Now we have to find for what value of `theta < 360`,
is the `sec theta = -3/2`

since we know `sec & cos` are reciprocal , we can state the above as
`cos theta = -2/3`

`theta = arc cos(-2/3)` = `131.8^@`

Answer 2

`131^@81; 228^@19`

Explanation:

2 - sec t = 5 + sec t
- 2sec t = 3
`sec t = -3/2`
`cos t = -2/3`
Calculator and unit circle give 2 solutions:
`t = +- 131^@81`
We know the arc (- 131.81) is co-terminal to arc
(360 - 131.81 = 228.19)
Answers for (0, 360)
`131^@81; 228^@19`