First slide

Multiple and sub- multiple Angles

Question

If $\sin 2 θ = \cos 3 θ and θ$ is an acute angle, then $\sin θ$ equals

Easy

A

$\frac{\sqrt{5} - 1}{4}$
B

$- (\frac{\sqrt{5} - 1}{4})$
C

$\frac{\sqrt{5} + 1}{4}$
D

$\frac{- \sqrt{5} - 1}{4}$

Solution

$\begin{array}{l} \sin 2 θ = \cos 3 θ \\ or 2 \sin θcos θ = 4 \cos^{3} θ - 3 \cos θ \\ or 2 \sin θ = 4 (1 - \sin^{2} θ) - 3 \\ or 4 \sin^{2} θ + 2 \sin θ - 1 = 0 \\ or \sin θ = \frac{\sqrt{5} - 1}{4} \end{array}$

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