This algebra 2 trig graphs quiz asks 10 multiple-choice questions on graphs of trigonometric functions, and each answer comes with a short explanation.
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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Answered: 0 / 10
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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How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
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.
How to use this algebra 2 trig graphs quiz
Retake this algebra 2 trig graphs quiz until every answer is right, then move on to the worksheet and the test.
