Graphs of Trigonometric Functions

Grade 10·21 problems·~35 min·ACT Math·topic·act-geo-trig-graphs

Work through problems with immediate feedback

Recall / Warm-Up

What is the value of $\sin\!\left(\frac{\pi}{2}\right)$ ?

-1

$\frac{1}{2}$

What is the value of $\cos(\pi)$ ?

-1

$\frac{\sqrt{2}}{2}$

How many radians are in a full rotation around the unit circle?

$\pi$

$2\pi$

360

$\frac{\pi}{2}$

$Graph of y=4sin(x) with amplitude 4 labeled with dashed lines at y=4 and y=-4.$

What is the amplitude of $y = 4\sin(x)$ ?

$\frac{\pi}{2}$

$2\pi$

$Graph of y=sin(3x) showing three cycles with period 2π/3 annotated.$

What is the period of $y = \sin(3x)$ ?

$3$

$6\pi$

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

$\frac{\pi}{3}$

What is the period of $y = \cos(4x)$ ? Express your answer in terms of $\pi$ .

$y=sin(2x) (gray dashed) and y=sin(2x-π) (teal solid) showing the π/2 rightward phase shift.$

What is the phase shift of $y = \sin(2x - \pi)$ ?

$\pi$ to the left

$\pi$ to the right

$\frac{\pi}{2}$ to the left

$\frac{\pi}{2}$ to the right

$Graph of y=3cos(x)+5 showing midline y=5, maximum y=8, minimum y=2, and amplitude 3.$

What are the amplitude and midline of $y = 3\cos(x) + 5$ ?

Amplitude $= 3$ , midline $y = 5$

Amplitude $= 5$ , midline $y = 3$

Amplitude $= 3$ , midline $y = 0$

Amplitude $= 8$ , midline $y = 5$

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