Precalculus Trigonometric Identities Test with Point Values (PDF)

Precalculus math test: Trigonometric Identities – Maths PDF

Cover of the book Precalculus Math Tests with Answer Keys (PDF)

Download as a PDFThe Precalculus tests book with answer keysPrintable PDFSee the book ›

Sommaire

This trig identities test for Precalculus covers trigonometric identities (Common Core F-TF.C.8, F-TF.C.9), with a free PDF to print.

This 20-point test covers the Pythagorean identity, sum and double-angle formulas, verifying identities, solving equations and a projectile model (F-TF.C.8, F-TF.C.9). You have 45 minutes. Show your work.

Time and points

About this test

Grade: Precalculus
Chapter: Trigonometric Identities
Standards: F-TF.C.8, F-TF.C.9
Time: 45 minutes
Total: 20 points

Trig identities test: questions

Question 1 – Simplify [2 pts]

Simplify \(\frac{\sin^{2}x}{1-\cos x}\) to a form with no fraction.

Question 2 – Exact value [2 pts]

Find the exact value of \(\cos75^{\circ}\).

Question 3 – Double angle [2 pts]

If \(\cos\theta=\frac{5}{13}\) and \(\theta\) is in quadrant IV, find \(\sin2\theta\) and \(\cos2\theta\).

Question 4 – Verify [2 pts]

Verify \(\frac{1-\cos2x}{2\sin x}=\sin x\).

Question 5 – Angle addition [3 pts]

Two acute angles.

Acute angles \(\alpha\) and \(\beta\) have \(\sin\alpha=\frac{8}{17}\) and \(\cos\beta=\frac35\). Find (a) \(\sin(\alpha+\beta)\); (b) \(\cos(\alpha+\beta)\); (c) \(\tan(\alpha+\beta)\).

Question 6 – Solve [2 pts]

Solve \(\sin2x=\cos x\) for \(0\le x< 2\pi\).

Question 7 – Solve with cos 2x [2 pts]

Graph of y = cos 2x and y = 1/2.

Solve \(\cos2x=\frac12\) for \(0\le x< 2\pi\).

Question 8 – Projectile range [3 pts]

Range against launch angle.

A ball launched at \(96\) ft/s with angle \(\theta\) has range \(R=\frac{96^{2}\sin2\theta}{32}\) feet. (a) Find \(R\) at \(15^{\circ}\). (b) Find \(R\) at \(45^{\circ}\). (c) Find another angle with the same range as \(15^{\circ}\).

Question 9 – Verify a Pythagorean form [2 pts]

Verify \((1+\tan^{2}x)\cos^{2}x=1\).

Key facts behind this trig identities test

Key facts

sin^2 x + cos^2 x = 1 and 1 + tan^2 x = 1/cos^2 x.
tan x = sin x / cos x; csc, sec, cot are reciprocals of sin, cos, tan.
sin(A + B) = sin A cos B + cos A sin B; cos(A + B) = cos A cos B – sin A sin B.
sin 2A = 2 sin A cos A; cos 2A = cos^2 A – sin^2 A = 1 – 2 sin^2 A = 2 cos^2 A – 1.
To verify an identity, work on one side only until it matches the other.

How to use this trig identities 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 Precalculus chapters: Precalculus math.

Voter.. post

Free printable PDF