Algebra 2 Graphs of Trigonometric Functions and Identities Test with Point Values (PDF)

Algebra 2 math test: Graphs of Trigonometric Functions and Identities – Maths PDF

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This algebra 2 trig graphs test for Algebra 2 covers graphs of trigonometric functions and identities (Common Core F-TF.B.5, F-TF.C.8, F-IF.C.7e), with a free PDF to print.

This 45-minute test on graphs of trigonometric functions and the Pythagorean identity has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Graphs of Trigonometric Functions and Identities
Standards: F-TF.B.5, F-TF.C.8, F-IF.C.7e
Time: 45 minutes
Total: 20 points

Algebra 2 trig graphs test: questions

Question 1 – Read the parameters [2 pts]

State the amplitude, period, and midline of \(y = 4\cos(3x) – 2\).

Question 2 – Equation from a graph [3 pts]

A cosine graph.

The graph shows a cosine-type wave with amplitude 3, midline \(y = 0\), and period \(4\pi\), starting at its maximum. Write the equation.

Question 3 – Ferris wheel [2 pts]

Rider’s height in feet over 60 seconds.

A rider’s height is \(h(t) = 25 – 20\cos\left(\frac{\pi}{15}t\right)\) feet. Find the height at \(t = 5\) seconds and the maximum height.

Question 4 – Cosine from sine [2 pts]

If \(\sin\theta = \frac{5}{13}\) and \(\theta\) is in quadrant II, find \(\cos\theta\).

Question 5 – Simplify [2 pts]

Simplify \(\cos^{2}x\,(1 + \tan^{2}x)\). Use \(\tan x = \frac{\sin x}{\cos x}\).

Question 6 – Write an equation [3 pts]

Write a cosine function for a quantity with maximum 10, minimum 2, and period 8, starting at the maximum.

Question 7 – Tides [2 pts]

A tide model is \(y = 3\sin\left(\frac{\pi}{6}t\right) + 5\) feet. Find the period and the high-tide height.

Question 8 – Quadrant IV [2 pts]

The right triangle in the unit circle: cos² θ + sin² θ = 1.

If \(\cos\theta = \frac{3}{5}\) and \(\theta\) is in quadrant IV, find \(\sin\theta\) and \(\tan\theta\).

Question 9 – Find the error [2 pts]

Mei says \(y = 2\sin x + 3\) has a minimum of 1 and a maximum of 5. Is she correct? Explain.

Key facts behind this algebra 2 trig graphs test

Key facts

Sine and cosine have period 2π and range -1 to 1.
y = A sin(B(x – C)) + D: amplitude |A|, period 2π/B, shift C, midline D.
Model cycles with a sinusoid: midline = average of max and min.
sin² θ + cos² θ = 1.
The quadrant gives the sign of the missing trig value.

How to use this algebra 2 trig graphs test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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