Question

Question #94f10

Answer 1

`theta = (1/3)(+-(2n+1)pi-pi/2)`, n = 0, 1, 2, 3..= `pi/6, 5pi/6, 9pi/6, 13pi/6, ...`. The negative solutions are `-3pi/6, -7pi/6, -11pi/6, ....`

Explanation:

The general value of `cos^(-1)(-1)` = an odd multiple of `pi`.

So, `3theta+pi/2` = an odd multiple of `pi` = `+-(2n+1)pi`, n = 0, 1, 2, 3, ...

Positive solutions are `pi/6, 5pi/6, 9pi/6, 13pi/6, ...`
The negative solutions are `-3pi/6, -7pi/6, -11pi/6, ....`

Answer 2

`t = pi/2 + k.pi`

Explanation:

Trig unit circle gives -->
`cos (3t + pi/2) = - 1 = cos pi`
`3t + pi/2 = +- pi`
a. `3t = pi - pi/2 = pi/2`. --->`t = (3pi)/2`
b. `3t = -pi - pi/2 = -(3pi)/2`, or `(pi/2)` --> co-terminal
General answers:
`t = pi/2 + k.pi`