Question

How do you find the solution to `3cos^2theta-4costheta+1=0` if `0<=theta<360`?

Answer 1

`0^@, 70^@53, 289^@47, 369^@`

Explanation:

`3cos^2 t - 4cos t + 1 = 0`
Solve the quadratic equation for cos t.
We have: a = 3, b = -4, and c = 1.
Since a + b + c = 0, use shortcut. The 2 real roots are:
cos x = 1 and `cos x = c/a = 1/3`
a. cos x = 1 --> `x = 0^@` or `x = 360^@`
b. `cos x = 1/3` --> Calculator and unit circle give 2 solutions arcs:
`x = 70^@53` and `x = - 70^@53`, or `x = 289^@47` (co-terminal)

Answers for (0, 360):
`0^@, 70^@53, 289^@47, 360^@`