Question

Given that sin 60 = root3/2
Find the exact value of sin 240

Answer 1

`sin 240^\circ = - (√(3))/(2)`

Explanation:

We are given that:

`sin 60^\circ = (√(3))/(2)`

We need to find

`sin 240^\circ = ?`

240 is greater than 180 and lesser than 270

OR

`180^\circ<240^\circ<270^\circ`

So, Angle
`240 ^\circ` lies in the 3rd quadrant and it is well known that value of sine in 3rd quadrant is negative.

Using the property :

`sin(\pi + \theta) = -sin\theta` or

`sin(180^\circ + \theta) = -sin\theta`

Here,
`\theta\ is\ 60^\circ`.

`sin 240^\circ =sin(180^\circ + 60^\circ) = -sin60^\circ\\\Rightarrow -(√(3))/(2)`

Hence, the value

`sin 240^\circ = - (√(3))/(2)`