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]}