Question

How do you find the exact value of `2costheta=sectheta` in the interval `0<=theta<360`?

Answer 1

`45^@, 135^@, 225^@, 315^@`

Explanation:

`2cos t = sec t = 1/(cos t)`
`2cos^2 t = 1`
`cos^2 t = 1/2` --> `cos t = +- 1/sqrt2 = +- sqrt2/2`
Use trig table and unit circle -->
a. `cos t = sqrt2/2` --> arc `t = +- pi/4` -->
`t = pi/4 and t = (7pi)/4` (co-terminal to `-pi/4`)

b. `cos t = - sqrt2/2` -->
arc `t = (3pi)/4, and t = (5pi)/4`
Answers for `(0, 2pi)`:
`pi/4, (3pi)/4, (5pi)/4, (7pi)/4`, or
Answers in degrees:
`45^@, 135^@, 225^@, 315^@`