Unit Circle & Radians Quiz: Sinusoids, Period, Arc Length

Question 1

A circle has radius $r=6$. What is the arc length subtended by a central angle of $	heta=\frac{5\pi}{6}$ radians?

Accepted Answer

$5\pi$

Answer

$30\pi$

Answer

$\frac{5\pi}{6}$

Answer

$10\pi$

Question 2

What is the period of $g(x)=\cos\left(\frac{3}{2}x\right)$?

Accepted Answer

$\frac{4\pi}{3}$

Answer

$\frac{3\pi}{2}$

Answer

$3\pi$

Answer

$\frac{2\pi}{3}$

Question 3

A sinusoid has maximum value $7$ and minimum value $-1$. Its period is $\frac{2\pi}{3}$ and it crosses its midline going upward at $x=\frac{\pi}{6}$. Which function could represent it?

Accepted Answer

$y=3\sin\left(3\left(x-\frac{\pi}{6}\right)\right)+3$

Answer

$y=4\cos\left(3\left(x-\frac{\pi}{6}\right)\right)+3$

Answer

$y=4\sin\left(\frac{2\pi}{3}\left(x-\frac{\pi}{6}\right)\right)+3$

Answer

$y=4\sin\left(3x-\frac{\pi}{6}\right)+3$

Unit Circle & Radians Quiz: Sinusoids, Period, Arc Length

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