Question

If sin theta=-1/4 and theta terminates in the third quadrant, find the exact value of sin2 theta.

Answer 1

Answer:

$sin(2\theta)=\frac{\sqrt{15}}{8}$

Step-by-step explanation:

We are given

$sin(\theta)=-\frac{1}{4}$

Firstly, we can draw triangle

angle lies in third quadrant

so, we get

$cos(\theta)=-\frac{\sqrt{15} }{4}$

now, we can use formula

$sin(2\theta)=2sin(\theta)\times cos(\theta)$

now, we can plug values

$sin(2\theta)=2\times -\frac{1}{4}\times -\frac{\sqrt{15} }{4}$

now, we can simplify it

and we get

$sin(2\theta)=\frac{\sqrt{15}}{8}$

Answer 2

Answer:

$\frac{\sqrt{15} }{8}$  or  sqrt15/8