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• Trigonometry
• Graphing Trig Functions
• Graph of the sine and cosine

# Graph of the sine and cosine

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•  Question 1: 1 pts Which graph is sketched in the given image.
 $y=2\sin x$ $y=\sin x$ $y=\cos x$ $y=\tan x$
•  Question 2: 1 pts Which graph is sketched in the given image.
$f(x)=$
•  Question 3: 1 pts $\sin x$ is an odd function and its graph is symmetric with respect to the origin $(0 , 0).$
•  Question 4: 1 pts $\cos x$ is an even function and its graph is symmetric with respect to the $x$ axis.
•  Question 5: 2 pts In the interval $0 < x\leq \pi$ for what values of $x$ is the graph of $y=\sin x$ increasing?
It is increasing on the interval
•  Question 6: 2 pts Determine the range of the function shown on the graph.
Range:
•  Question 7: 2 pts Select the interval where $g$ is decreasing.
 $2 < x < 3$ $-1 < x < 3$ $-1 < x < 1$ $3 < x < 5$
•  Question 8: 2 pts Find the zeros of the sine function $f(x)=\sin x-\dfrac{1}{2}.$
 $x=\dfrac{\pi}{6}+2k\pi \mbox{and} \dfrac{5\pi}{6}+2k\pi, k \in \mathbb{Z}$ $x=\dfrac{\pi}{6}+2k\pi, k \in \mathbb{Z}$ $x=\dfrac{\pi}{3}+2k\pi, k \in \mathbb{Z}$ $x=\dfrac{\pi}{3}+k\pi \mbox{and} \dfrac{5\pi}{6}+2k\pi, k \in \mathbb{Z}$
•  Question 9: 3 pts Determine the range of the function $f(x)=0.5\sin \left(\dfrac{x}{\pi}+\pi \right)-2$ shown on the graph.
Range:
•  Question 10: 3 pts Determine phase shift for the function $y=2\sin (6x-2)+3.$
Phase shift:
•  Question 11: 3 pts Determine phase shift for the function $y=\cos \left(x+\dfrac{\pi}{4}\right)$.
Phase shift:
•  Question 12: 2 pts Which graph is sketched in the given image.
 $2\cos |x|$ $y=\cos |x|$ $y=|\cos x|$ none of these