Question

18 multiple choice 1 point find the cosine and sine of 210°. round your answers to the nearest hundredth if necessary. -0.87, -0.5 -1,0 -0.55, -0.95 -0.5, -0.87

Explanation:

Step1: Determine the reference angle

The reference angle for \(210^{\circ}\) is \(210^{\circ}- 180^{\circ}=30^{\circ}\).

Step2: Use the unit - circle values and signs

In the third quadrant (\(180^{\circ}<\theta <270^{\circ}\)), both \(\cos\theta\) and \(\sin\theta\) are negative.
We know that \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\approx0.87\) and \(\sin30^{\circ}=\frac{1}{2} = 0.5\).
So, \(\cos210^{\circ}=-\cos30^{\circ}\approx - 0.87\) and \(\sin210^{\circ}=-\sin30^{\circ}=-0.5\)

Answer:

-0.87, - 0.5