Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree. (Enter your answers as a comma-separated list.)? 3 sin^2 θ − 10 cos 2theta = 0

3 sin^2 θ − 10 cos 2theta = 0

1 Answer
Aug 9, 2018

theta= 41.3^@, 138.7^@, 221.3^@, 318.7^@

Explanation:

3sin^2theta-10(1-2sin^2theta)= 0

23sin^2theta-10=0

sin^2theta= 10/23

sintheta= +-sqrt(10/23)

theta= arcsin(sqrt(10/23))=41.3^@

theta= arcsin(-sqrt(10/23))=-41.3^@+360^@=318.7^@

We missed the solutions in quadrants 2 and 3 as arcsin is restricted to quadrants 1 and 4:

So:
41.3^@+180^@= 221.3^@

318.7^@-180^@= 138.7^@

graph{3(sinx)^2-10cos(2x) [-10, 10, -5, 5]}