First slide

Trigonometric Identities

Question

If $\tan θ = 3$ and $θ$ lies in third quadrant, then the value of $\sin θ$ is

Moderate

A

$\frac{1}{\sqrt{10}}$
B

$- \frac{1}{\sqrt{10}}$
C

$- \frac{3}{\sqrt{10}}$
D

$\frac{3}{\sqrt{10}}$

Solution

$\tan θ = 3 \Rightarrow \sin θ = 3 \cos θ \Rightarrow \sin^{2} θ = 9 \cos^{2} θ = 9 (1 - \sin^{2} θ) \Rightarrow \sin θ = - \frac{3}{\sqrt{10}}$

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