Graphs of Trigonometric Functions: Algebra 2 Math Quiz – PDF Download
Answer these 10 multiple-choice questions on graphs of sine and cosine. They cover amplitude, period, midline, phase shift, reading graphs and periodic models. Choose one answer for each question, then check the explanations.
Algebra 2Common Core: F-TF.B.5 · F-IF.C.7e
🎯 Graphs of Trigonometric Functions – Algebra 2 math quiz
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Question 1
What is the amplitude of \(y=-5\sin x+2\)?
A\(-5\)
B\(2\)
C\(7\)
D\(5\)
Question 2
What is the period of \(y=\cos(3x)\)?
A\(6\pi\)
B\(2\pi\)
C\(\frac{2\pi}{3}\)
D\(\frac{\pi}{3}\)
Question 3
Which equation matches the graph?Graph for quiz question 3.
A\(y=3\sin x+1\)
B\(y=3\cos x+1\)
C\(y=4\cos x-2\)
D\(y=\cos(3x)+1\)
Question 4
What is the midline of \(y=4\sin x-3\)?
A\(y=3\)
B\(y=-3\)
C\(y=4\)
D\(y=-4\)
Question 5
Which equation matches the graph?Graph for quiz question 5.
A\(y=2\sin\left(x+\frac{\pi}{3}\right)\)
B\(y=2\sin x-\frac{\pi}{3}\)
C\(y=2\sin\left(x-\frac{\pi}{3}\right)\)
D\(y=2\cos\left(x-\frac{\pi}{3}\right)\)
Question 6
What is the range of \(y=-2\cos x+3\)?
A\([1,5]\)
B\([-5,-1]\)
C\([-2,2]\)
D\([3,5]\)
Question 7
The graph shows the height of a water wheel paddle. What is the period?Graph for quiz question 7.
A\(10\) seconds
B\(5\) seconds
C\(20\) seconds
D\(4\) seconds
Question 8
A sine wave \(y=\sin(Bx)\) has period \(8\). What is \(B\)?
A\(8\pi\)
B\(\frac{\pi}{8}\)
C\(\frac{\pi}{2}\)
D\(\frac{\pi}{4}\)
Question 9
What is \(f\left(\frac{3\pi}{2}\right)\) for \(f(x)=2\sin x-1\)?
A\(-3\)
B\(1\)
C\(-1\)
D\(-2\)
Question 10
A model is \(h(t)=12+8\cos\left(\frac{\pi t}{5}\right)\). What is the minimum height?
A\(8\)
B\(4\)
C\(12\)
D\(20\)
🎉 Quiz complete!
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Remember:
Standards F-TF.B.5 and F-IF.C.7e: graph sine and cosine and use them to model periodic phenomena.
Parent functions have amplitude \(1\), period \(2\pi\), midline \(y=0\) and range \([-1,1]\).
Period is \(\frac{2\pi}{B}\): a larger \(B\) squeezes the wave horizontally.
Maximum \(=D+|A|\) and minimum \(=D-|A|\), so \(D=\frac{\max+\min}{2}\).
To model a situation, match the radius or half-range to \(A\), the center to \(D\) and the time per cycle to the period.
