Question

If 5 cos^2 0 + 6 sin^2 0 = 11/2, then sin 0 =

Answer 1

Step-by-step explanation:

$5 \cos {}^{2} ( \alpha ) + 5 \sin {}^{2} ( \alpha ) + \sin {}^{2} ( \alpha ) = \frac{11}{2} \\ 5( \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) ) + \sin {}^{2} ( \alpha ) = \frac{11}{2} \\ 5(1) + \sin {}^{2} ( \alpha ) = \frac{11}{2} \\ \sin {}^{2} ( \alpha ) = \frac{11}{2} - 5 \\ \sin {}^{2} ( \alpha ) = \frac{1}{2} \\ \sin( \alpha ) = \sqrt{ \frac{1}{2} } \\ \sin( \alpha ) = \frac{1}{ \sqrt{2} } \\ hence \: \: \alpha = 45$