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

1.	Find the acute angle theta such that 2 cos squared theta is equal to 3 sin theta
Answer» Answer: 30 deg Step-by-step explanation: $2 \cos ^{2} ( \<klux>ALPHA</klux> ) = 3 \sin( \alpha ) \\ 2 (<klux>1</klux> - \sin ^{2} ( \alpha )) = 3 \sin( \alpha )$ $2 \sin^{2} ( \alpha ) + 3 \sin( \alpha ) - 2 = 0 \\ 2 \sin^{2} ( \alpha ) + 4 \sin( \alpha ) - \sin( \alpha ) - 2 = 0 \\ 2 \sin( \alpha ) ( \sin( \alpha ) + 2) - 1( \sin( \alpha ) + 2) = 0$ $(2 \sin( \alpha ) - 1)( \sin( \alpha ) + 2) = 0$ sin alpha LIES between -1 & 1 $\sin( \alpha ) = \frac{1}{2}$ $\alpha = 30deg$

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

Answer»

Answer:

30 deg

Step-by-step explanation:

$2 \cos ^{2} ( \<klux>ALPHA</klux> ) = 3 \sin( \alpha ) \\ 2 (<klux>1</klux> - \sin ^{2} ( \alpha )) = 3 \sin( \alpha )$

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