Question

Question #3837a

Answer 1

x = pi/2 + 2kpi
x = (3pi)/2 + 2kpi
x = +- pi/3 + 2kpi

Explanation:

`48sin^2 x = 48 - 24cos x`
Replace `sin^2 x` by `1 - cos^2 x`:
`48 - 48cos^2 x = 48 - 24cos x`
`48 cos^2 x - 24 cos x = 0`
`24cos x(2cos x - 1) = 0`
Either factor should be zero.
a. cos x = 0. Unit circle gives 2 solutions
`x = pi/2 + 2kpi`, and `x = (3pi)/2 + 2kpi`
b. 2cos x = -1 -->`cos x = 1/2`
Trig table and unit circle give 2 solutions:
`x = +- pi/3 + 2kpi`