First slide

Trigonometric equations

Question

General solutions of the equations $\sin x = \frac{- 1}{2}$ and $\cos x = \frac{- \sqrt{3}}{2}$ is

Easy

A

$x = 2 n π + \frac{π}{6}$
B

$x = 2 n π + \frac{5 π}{6}$
C

$x = 2 n π + \frac{7 π}{6}$
D

$x = 2 n π + \frac{11 π}{6}$

Solution

We have $\sin x = \frac{- 1}{2} < 0$ and $\cos x = \frac{- \sqrt{3}}{2} < 0$
$∴$ x belongs to 3rd quadrant and $x = π + \frac{π}{6} = \frac{7 π}{6}$
$∴$ General solution is $x = 2 n π + \frac{7 π}{6}, n \in z$

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