Question

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

Answer 1

`sin(2\theta)=(√(15))/(8)`

Explanation:

We are given

`sin(\theta)=-(1)/(4)`

Firstly, we can draw triangle

angle lies in third quadrant

so, we get

`cos(\theta)=-(√(15) )/(4)`

now, we can use formula

`sin(2\theta)=2sin(\theta)* cos(\theta)`

now, we can plug values

`sin(2\theta)=2* -(1)/(4)* -(√(15) )/(4)`

now, we can simplify it

and we get

`sin(2\theta)=(√(15))/(8)`

Answer 2

`(√(15) )/(8)` or sqrt15/8