First slide

Trigonometric equations

Question

General solution of simultaneous equations $\tan θ = \frac{- 1}{\sqrt{3}}$ and $\cos θ = \frac{\sqrt{3}}{2}$ is

Easy

A

$θ = n π + \frac{π}{6}, n \in z$
B

$θ = n π + \frac{11 π}{6}, n \in z$
C

$θ = 2 n π + \frac{π}{3}, n \in z$
D

$θ = 2 n π + \frac{11 π}{6}, n \in z$

Solution

We have $\tan θ = - \frac{1}{\sqrt{3}} < 0, \cos θ = \frac{\sqrt{3}}{2} > 0$
$∴$ $θ$ belongs to 4th quadrant and it is $2 π - \frac{π}{6} = \frac{11 π}{6}$
$∴$ general solution is $θ = 2 n π + \frac{11 π}{6}, n \in z$

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