How do you calculate #sin (-150°)#?

Question

13910 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-21T14:37:02

#-1/2#

#\sin(-150^\circ)#

#=-\sin(150^\circ)#

#=-\sin(180^\circ-30^\circ)#

#=-\sin(30^\circ)\quad (\because \ \sin(180^\circ-\theta)=\sin\theta)#

#=-1/2#

Answer 2 · 2018-07-21T15:33:30

#-1/2#

Recall the negative angle identity

#sin(-theta)=-sin(theta)#

With this in mind, we can rewrite #sin(-150)# as #-sin(150)#.

#150^@# has a reference angle of #30^@#, which means it will have the same trig values as #30^@#.

On the Unit Circle, we know the coordinates for #30^@# are #(sqrt3/2,1/2)#, where the #y#-coordinate is the #sin# value.

This means #sin(-150)=-1/2#

Hope this helps!