Evaluate the expression using the concept of a reference angle. $\sin \left( - 150 ^ { \circ } \right)$
A) $\frac { \sqrt { 6 } } { 6 }$
B) $\frac { \sqrt { 6 } } { 2 }$
C) $\frac { 1 } { 2 }$
D) $- \frac { 1 } { 2 }$
E) $- \frac { 1 } { 6 }$

Question

Quizplus · Accepted Answer

To find the reference angle for -150 degrees, we want to find the acute angle between the terminal side of -150 degrees and the x-axis in standard position. We can do this by subtracting 180 degrees (or pi radians) from the absolute value of -150 degrees:

| -150 | - 180 = 30

So the reference angle for -150 degrees is 30 degrees.

Since sine is negative in the third quadrant, we can use the reference angle to find the value of sine for -150 degrees:

sin(-150) = - sin(30) = -1/2

Therefore, the best choice is D, -1/2.

Evaluate the Expression Using the Concept of a Reference Angle sin⁡(−150∘)\sin \left( - 150 ^ { \circ } \right)sin(−150∘)

Evaluate the Expression Using the Concept of a Reference Angle $\sin \left( - 150 ^ { \circ } \right)$