First slide

Trigonometric equations

Question

The solution set of $\sin 2 θ = \frac{- 1}{\sqrt{2}}$ is

Easy

A

${\frac{n π}{2} + {(- 1)}^{n + 1} \frac{π}{6} : n \in Z}$
B

${\frac{n π}{2} + {(- 1)}^{n} \frac{π}{12} : n \in Z}$
C

${\frac{n π}{3} + {(- 1)}^{n} \frac{2 π}{15} : n \in Z}$
D

${\frac{n π}{2} + {(- 1)}^{n + 1} \frac{π}{8} : n \in Z}$

Solution

$\sin 2 θ = \frac{- 1}{\sqrt{2}} = \sin (- \frac{π}{4}) \Rightarrow 2 θ = n π + {(- 1)}^{n} (- \frac{π}{4}) \Rightarrow θ = \frac{nπ}{2} + {(- 1)}^{n + 1} (\frac{π}{8})$

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