How to calculate sin ( - 150 ° ) ?

Question

How to calculate             sin              (        -        150        °        )            ?

objesilo5lr1 · Accepted Answer

Given solution:             sin              (        -                  150          ∘                )                  =    -          sin              (                  150          ∘                )                  =    -          sin              (                  180          ∘                -                  30          ∘                )                  =    -          sin              (                  30          ∘                )                          (      ∵                     sin                  (                      180            ∘                    -          θ          )                    =              sin        θ            )            =    -          1      2

daneetuhxxtj · Accepted Answer

Recall the identification of the negative angle.

\sin (- θ) = - \sin (θ)

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

150^{\circ}

has a reference angle of

30^{\circ}

, which means it will have the same trig values as

30^{\circ}

On the Unit Circle, we know the coordinates for

30^{\circ}

are

(\frac{\sqrt{3}}{2}, \frac{1}{2})

, where the #y#-coordinate is the

\sin

value.
This implies

\sin (- 150) = - \frac{1}{2}

How to calculate sin (-150°)?

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