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.)? $3 sin^2 θ − 10 cos 2theta = 0$

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$3 sin^2 θ − 10 cos 2theta = 0$

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Answer 1 · 2018-08-09T06:09:15

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

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

$23sin^2theta-10=0$

$sin^2theta= 10/23$

$sintheta= +-sqrt(10/23)$

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

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

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]}