114k views
5 votes
Given that sin 60 = root3/2
Find the exact value of sin 240

Given that sin 60 = root3/2 Find the exact value of sin 240-example-1

1 Answer

4 votes

Answer:


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)

User Jacobhyphenated
by
8.4k points

Related questions

1 answer
3 votes
46.7k views
asked Aug 18, 2024 162k views
Vps asked Aug 18, 2024
by Vps
8.9k points
1 answer
1 vote
162k views