Question

find the acute angle theta such that 2 cos squared theta is equal to 3 sin theta

Answer 1

Answer:

2cos^2theta = 3sin theta

Answer 2

Answer:

30 deg

Step-by-step explanation:

$2 \cos ^{2} ( \alpha ) = 3 \sin( \alpha ) \\ 2 (1 - \sin ^{2} ( \alpha )) = 3 \sin( \alpha )$

$2 \sin^{2} ( \alpha ) + 3 \sin( \alpha ) - 2 = 0 \\ 2 \sin^{2} ( \alpha ) + 4 \sin( \alpha ) - \sin( \alpha ) - 2 = 0 \\ 2 \sin( \alpha ) ( \sin( \alpha ) + 2) - 1( \sin( \alpha ) + 2) = 0$

$(2 \sin( \alpha ) - 1)( \sin( \alpha ) + 2) = 0$

sin alpha lies between -1 & 1

$\sin( \alpha ) = \frac{1}{2}$

$\alpha = 30deg$