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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.
$f(x)=$
$2\sin x$
$\sin x$
$\cos x$
$\tan x$
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
$\left(\dfrac{\pi}{3},\pi\right)$
$\left(\dfrac{\pi}{3},\dfrac{\pi}{2}\right)$
$\left(0,\dfrac{\pi}{2}\right)$
$\left(\dfrac{\pi}{2},\pi\right)$
Question 6:
2 pts
Determine the range of the function shown on the graph.
Range:
$[-1,2]$
$[1,2]$
$[-1,1]$
$[-2,2]$
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:
$[-1.9,1.9]$
$[-2.5,-1,5]$
$[-1.9,2.1]$
$[-2.5,-2.1]$
Question 10:
3 pts
Determine phase shift for the function $y=2\sin (6x-2)+3.$
Phase shift:
$\dfrac{\pi}{2}$ to the left
$\dfrac{1}{3}$ to the right
$\dfrac{\pi}{4}$ to the right
$\pi$ to the left
Question 11:
3 pts
Determine phase shift for the function $y=\cos \left(x+\dfrac{\pi}{4}\right)$.
Phase shift:
To the left by $\dfrac{\pi}{4}$
To the right by $\dfrac{\pi}{4}$
To the left by $\dfrac{\pi}{2}$
To the right by $\dfrac{\pi}{2}$
Question 12:
2 pts
Which graph is sketched in the given image.
$2\cos |x|$
$y=\cos |x|$
$y=|\cos x|$
none of these
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