Question

How do you know if $\sin 30°=\sin 150°$?

Answer 1

Explanation with unit circle:

All trigonometric angles are determined with respect to the given unit circle.

The reference angle for $150°$ is equal to $30°$ for the triangle formed in the unit circle.

The reference angle is formed when the perpendicular is dropped from the unit circle to the $x$-axis, which forms a right triangle.

Since the angle $150°$ degrees lies on the IInd quadrant, therefore the value of $\sin 150°$ is positive.

The internal angle of the triangle is $180°–150°=30$, which is the reference angle.

The value of sine in the other two quadrants, i.e. 3rd and 4th are negative.

Hence, it can be said that $\mathbf{sin}\mathbf{}\mathbf{30}\mathbf{°}\mathbf{}\mathbf{=}\mathbf{}\mathbf{sin}\mathbf{}\mathbf{150}\mathbf{°}$.