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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

Angle Measurement

Right triangle

Unit circle

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