Question

review passage
find the sine and cosine of the given angle
question
210°
select a single answer
cos(210°) = -√3/2, sin(210°) = -1/2
cos(210°) = √3/2, sin(210°) = 1/2
cos(210°) = 1/2, sin(210°) = -√3/2
cos(210°) = -1/2, sin(210°) = √3/2

Explanation:

Step1: Find reference angle

$210^{\circ} - 180^{\circ} = 30^{\circ}$

Step2: Identify quadrant sign rules

In Q3, $\sin<0$, $\cos<0$

Step3: Use reference angle values

$\sin(30^{\circ})=\frac{1}{2}$, so $\sin(210^{\circ})=-\frac{1}{2}$
$\cos(30^{\circ})=\frac{\sqrt{3}}{2}$, so $\cos(210^{\circ})=-\frac{\sqrt{3}}{2}$

Answer:

$\cos(210^{\circ}) = -\frac{\sqrt{3}}{2}, \sin(210^{\circ}) = -\frac{1}{2}$