Question

13 multiple choice 1 point
find the cosine and sine of 120°. round your answers to the nearest hundredth if necessary.
-0.87, 0.5
-0.5, 0.87
0.95, -0.55
0, 1

Explanation:

Step1: Use the unit - circle and reference - angle concept

The angle \(120^{\circ}\) has a reference angle \(\theta'=180^{\circ}- 120^{\circ}=60^{\circ}\).
In the second quadrant, \(\cos\theta<0\) and \(\sin\theta>0\).

Step2: Calculate \(\cos120^{\circ}\)

We know that \(\cos\theta=-\cos\theta'\) (for \(\theta = 120^{\circ}\), \(\theta'\) is the reference angle). Since \(\cos60^{\circ}=\frac{1}{2}=0.5\), then \(\cos120^{\circ}=-\cos60^{\circ}=- 0.5\).

Step3: Calculate \(\sin120^{\circ}\)

We know that \(\sin\theta=\sin\theta'\) (for \(\theta = 120^{\circ}\), \(\theta'\) is the reference angle). Since \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\approx0.87\), then \(\sin120^{\circ}=\sin60^{\circ}\approx0.87\).

Answer:

-0.5, 0.87