Question

Question #689a9

Answer 1

`pi/2; (7pi)/6; (11pi)/6`

Explanation:

cos 2t + sin t = 0
Substitute in the equation `cos 2t` by `(1 - 2sin^2 t)`:
`1 - 2sin^2 t + sin t = 0`
`- 2sin^2 t + sin t + 1 = 0`
Solve this quadratic equation for sin t
Since a + b + c = 0, use shortcut.
The 2 real roots are: sin t = 1 and `sin t = c/a = - 1/2`
Trig table and unit circle gives 3 solution:
a. sin t = 1 --> `t = pi/2`
b. `sin t = -1/2`, unit circle give 2 solutions:
`t = - pi/6` or, `t = (11pi)/6` (co-terminal),
and `t = pi - (- pi/6) = pi + pi/6 = (7pi)/6`