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AP Precalculus — Unit 3: Trigonometric and Polar Functions: 295 practice questions

295 original AP Precalculus questions on Unit 3: Trigonometric and Polar Functions, each with an explanation and its source. Topics: Sine, Cosine, and Tangent, The Tangent Function, Periodic Phenomena, Sine and Cosine Function Values, Sine and Cosine Function Graphs, Sinusoidal Functions, Sinusoidal Function Transformations, Trigonometric Equations and Inequalities, Trigonometry and Polar Coordinates, Sinusoidal Function Context and Data Modeling, Inverse Trigonometric Functions, Secant, Cosecant, and Cotangent Functions, Equivalent Representations of Trigonometric Functions, Polar Function Graphs, Rates of Change in Polar Functions, 3.6 Sinusoidal Function Transformations, 3.7 Sinusoidal Function Context and Data Modeling, 3.10 Trigonometric Equations and Inequalities, 3.12 Equivalent Representations of Trigonometric Functions, 3.1 Periodic Phenomena, 3.2 Sine, Cosine, and Tangent, 3.3 Sine and Cosine Function Values, 3.4 Sine and Cosine Function Graphs, 3.5 Sinusoidal Functions, 3.8 The Tangent Function, 3.9 Inverse Trigonometric Functions, 3.11 The Secant, Cosecant, and Cotangent Functions, 3.13 Trigonometry and Polar Coordinates, 3.14 Polar Function Graphs, 3.15 Rates of Change in Polar Functions, 3.11 Secant, Cosecant, and Cotangent Functions. Two free samples are below. Try 5 more free, no sign-up.

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Two Unit 3: Trigonometric and Polar Functions questions with explanations

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Q1 Sine, Cosine, and Tangent

On the unit circle, what is cos(5π/6)?

  1. −√3/2
  2. −1/2
  3. 1/2
  4. √3/2
Show the answer and explanation

Answer: A. The angle 5π/6 is in Quadrant II with reference angle π/6. Cosine is the x-coordinate and is negative in Quadrant II; its magnitude is √3/2.

Sources: College Board, AP Precalculus Course and Exam Description · College Board AP Central, AP Precalculus

Q2 The Tangent Function

What is the period of f(x)=tan(2x)?

  1. π/2
  2. π
  3. 2π
  4. 4π
Show the answer and explanation

Answer: A. The tangent function has base period π. Replacing x by 2x compresses the graph horizontally by a factor of 2, so the period is π/2.

Sources: College Board, AP Precalculus Course and Exam Description · College Board AP Central, AP Precalculus

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