Trigonometric Identities Question 333
Question: If $ \sin \alpha =\frac{336}{625} $ and $ 450{}^\circ <\alpha <540{}^\circ , $ then $ \sin ( \frac{\alpha }{4} )= $
Options:
A) $ \frac{1}{5\sqrt{2}} $
B) $ \frac{7}{25} $
C) $ \frac{4}{5} $
D) $ \frac{3}{5} $
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Answer:
Correct Answer: C
Solution:
$ \sin \alpha =\frac{336}{625} $
Þ $ \cos \alpha =-\sqrt{1-{{\sin }^{2}}\alpha }=-\sqrt{1-{{( \frac{336}{625} )}^{2}}} $ , [ $ \because $ $ \alpha $ is in II Quadrant] Now, $ \cos ( \frac{\alpha }{2} )=-\sqrt{\frac{1+\cos \alpha }{2}}=-\frac{7}{25} $ , [ $ \because \frac{\alpha }{2} $ is in III Quadrant]
$ \therefore ,\sin ( \frac{\alpha }{4} )=+\sqrt{\frac{1-\cos (\alpha /2)}{2}}=\sqrt{\frac{1+\frac{7}{25}}{2}}=\frac{4}{5} $ , [ $ \because ,\frac{\alpha }{4} $ is in II Quadrant]
BETA
