Question

1. reference angle

a. $-30^\circ$
b. $60^\circ$
c. $30^\circ$
d. $-60^\circ$
find the reference angle, sine, cosine, and tangent for $\theta = 330^\circ$. choose the correct answer.
close

Explanation:

Step1: Locate angle quadrant

$330^\circ$ is in Quadrant IV ($270^\circ < 330^\circ < 360^\circ$)

Step2: Calculate reference angle

Reference angle = $360^\circ - 330^\circ = 30^\circ$

Step3: Confirm trigonometric signs

In Quadrant IV, cosine is positive, sine/tangent negative.

Step4: Match to reference angle values

$\sin(330^\circ)=-\sin(30^\circ)=-\frac{1}{2}$, $\cos(330^\circ)=\cos(30^\circ)=\frac{\sqrt{3}}{2}$, $\tan(330^\circ)=-\tan(30^\circ)=-\frac{\sqrt{3}}{3}$; reference angle is $30^\circ$.

Answer:

C. $30^\circ$