Question

Which of the following expressions is equal to sin⁡⁡(-150°)?

sin(30°)
-sin(-30°)
-sin(30°)
sin(150°)

Answer 1

The answer is -sin(30°)
You can use calculator if you want to verify or to compare values if equal.

Answer 2

`sin (-150^(\circ))`=
`-sin30^(\circ)`

Explanation:

Given :
`sin (-150^(\circ))`

To Find: Which of the following expressions is equal to
`sin (-150^(\circ))`

Solution:

Property :
`sin(-x)=sinx`

So,
`sin (-150^(\circ))=-sin 150^(\circ)`

Now using identity :
`sin x = sin (180-x)`

So,
`-sin 150^(\circ) = -sin(180^(\circ)-150^(\circ))`

`-sin 150^(\circ) = -sin30^(\circ)`

Thus Option C is correct.

Hence
`sin (-150^(\circ))`=
`-sin30^(\circ)`