First slide

Trigonometric equations

Question

If $\sin θ = \frac{1}{2} and \cos θ = - \frac{\sqrt{3}}{2},$ then the general value of $θ is (n \in Z)$

Easy

A

$2 nπ + \frac{5 π}{6}$
B

$2 nπ + \frac{π}{6}$
C

$2 nπ + \frac{7 π}{6}$
D

$2 nπ + \frac{π}{4}$

Solution

$\begin{array}{l} \sin θ = 1 / 2 and \cos θ = - \sqrt{3} / 2 \\ \Rightarrow θ lies in the second quadrant. \\ \Rightarrow \sin θ = \sin 5 π / 6; \cos θ = \cos 5 π / 6; \\ ∴ θ = 2 nπ + (5 π / 6), n \in Z \end{array}$

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