Question

practice assignment 7.3 unit circle: sine and cosine
score: 7/12 answered: 7/12
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question 8
if $\theta = \frac { - 1 \pi } { 3 }$, then
$\sin ( \theta ) =$
$\cos ( \theta ) =$
give exact values. no decimals allowed!
question help: video 1 video 2

Explanation:

Step1: Use the property of sine function

The sine function has the property \(\sin(-x)=-\sin(x)\).
For \(\theta =-\frac{\pi}{3}\), we have \(\sin(-\frac{\pi}{3})=-\sin(\frac{\pi}{3})\).
Since \(\sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}\), then \(\sin(-\frac{\pi}{3})=-\frac{\sqrt{3}}{2}\).

Step2: Use the property of cosine function

The cosine function has the property \(\cos(-x)=\cos(x)\).
For \(\theta =-\frac{\pi}{3}\), we have \(\cos(-\frac{\pi}{3})=\cos(\frac{\pi}{3})\).
Since \(\cos(\frac{\pi}{3})=\frac{1}{2}\), then \(\cos(-\frac{\pi}{3})=\frac{1}{2}\).

Answer:

\(\sin(\theta)=-\frac{\sqrt{3}}{2}\), \(\cos(\theta)=\frac{1}{2}\)