3A. Trigonometric and Polar Functions
United States of America
AP Precalculus
3.3 Sine and cosine function values
Interactive practice questions
Consider the equation $y=\sin x$y=sinx.
a
Using the fact that $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$sinπ3=√32, what is the value of $\sin\frac{2\pi}{3}$sin2π3?
b
Using the fact that $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$sinπ3=√32, what is the value of $\sin\frac{4\pi}{3}$sin4π3?
c
Using the fact that $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$sinπ3=√32, what is the value of $\sin\frac{5\pi}{3}$sin5π3?
d
Complete the table of values. Give your answers in exact form.
| $x$x | $0$0 | $\frac{\pi}{3}$π3 | $\frac{\pi}{2}$π2 | $\frac{2\pi}{3}$2π3 | $\pi$π | $\frac{4\pi}{3}$4π3 | $\frac{3\pi}{2}$3π2 | $\frac{5\pi}{3}$5π3 | $2\pi$2π |
|---|---|---|---|---|---|---|---|---|---|
| $\sin x$sinx | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
e
Draw the graph of $y=\sin x$y=sinx.
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Medium
6min
Consider the equation $y=\cos x$y=cosx.
Medium
5min
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