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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=2sin⁡xy=2\sin x
    y=sin⁡xy=\sin x
    y=cos⁡xy=\cos x
    y=tan⁡xy=\tan x
  • Question 2:
    1 pts
    		Which graph is sketched in the given image.
    f(x)=f(x)=
  • Question 3:
    1 pts
    		sin⁡x\sin x is an odd function and its graph is symmetric with respect to the origin (0,0).(0 , 0).
  • Question 4:
    1 pts
    		cos⁡x\cos x is an even function and its graph is symmetric with respect to the xx axis.
  • Question 5:
    2 pts
    		In the interval 0<x≤π0 < x\leq \pi for what values of xx is the graph of y=sin⁡xy=\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 gg is decreasing.
    2<x<32 < x < 3
    −1<x<3-1 < x < 3
    −1<x<1-1 < x < 1
    3<x<53 < x < 5
  • Question 8:
    2 pts
    		Find the zeros of the sine function f(x)=sin⁡x−12.f(x)=\sin x-\dfrac{1}{2}.
    x=π6+2kπ\mboxand5π6+2kπ,k∈Zx=\dfrac{\pi}{6}+2k\pi \mbox{and} \dfrac{5\pi}{6}+2k\pi, k \in \mathbb{Z}
    x=π6+2kπ,k∈Zx=\dfrac{\pi}{6}+2k\pi, k \in \mathbb{Z}
    x=π3+2kπ,k∈Zx=\dfrac{\pi}{3}+2k\pi, k \in \mathbb{Z}
    x=π3+kπ\mboxand5π6+2kπ,k∈Zx=\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)=0.5sin⁡(xπ+π)−2f(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=2sin⁡(6x−2)+3.y=2\sin (6x-2)+3.
    Phase shift:
  • Question 11:
    3 pts
    		Determine phase shift for the function y=cos⁡(x+π4)y=\cos \left(x+\dfrac{\pi}{4}\right).
    Phase shift:
  • Question 12:
    2 pts
    		Which graph is sketched in the given image.
    2cos⁡∣x∣2\cos |x|
    y=cos⁡∣x∣y=\cos |x|
    y=∣cos⁡x∣y=|\cos x|
    none of these

Angle Measurement

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Unit circle

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