AP®MathsCollege BoardPrecalculusExam QuestionsTrigonometric & Polar FunctionsTrigonometric Functions

Trigonometric Functions (College Board AP® Precalculus): Exam Questions

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Trigonometric Functions

1
1 mark

The table gives selected values of the periodic function space f.

space t

0

2

4

6

8

10

12

space f open parentheses t close parentheses

5

8

5

2

5

8

5

Based on the values in the table, which of the following could be the period of space f?

  • 4

  • 6

  • 8

  • 10

Choose your answer

2
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1 mark

Which of the following angles has the same terminal ray in standard position as an angle of measure negative fraction numerator 3 pi over denominator 4 end fraction radians?

  • pi over 4

  • fraction numerator 3 pi over denominator 4 end fraction

  • fraction numerator 5 pi over denominator 4 end fraction

  • fraction numerator 7 pi over denominator 4 end fraction

Choose your answer

3
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1 mark

The figure shows a circle centered at the origin with an angle of measure \theta radians in standard position. The terminal ray of the angle intersects the circle at point P, and point Q also lies on the circle. The coordinates of P are open parentheses x comma space y close parentheses, and Q is a reflection of P in the y-axis. Which of the following gives the x-coordinate of Q?

A circle centred at O on a Cartesian plane, showing point P on the circle in the second quadrant and Q in the circle in the first quadrant, with right-angled triangles formed by dashed lines. Angle θ marked at the centre from the x-axis to the ray to point P.

  • negative 4 cos theta

  • 4 cos theta

  • 4 sin theta

  • negative 4 sin theta

Choose your answer

4
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1 mark

A circle is centered at the origin with radius 4. A point P starts at open parentheses 4 comma 0 close parentheses and travels a distance of 6 units along the circle in the counterclockwise direction. Which of the following gives the coordinates of P after this movement?

  • open parentheses 3.990 comma space 0.283 close parentheses

  • open parentheses 3.841 comma space minus 1.117 close parentheses

  • open parentheses 3.144 comma space 2.473 close parentheses

  • open parentheses 0.283 comma space 3.990 close parentheses

Choose your answer

5
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1 mark

The function g is given by g \left(x\right) = 2 \tan \left(\frac{x}{3}\right) + 1. What is the period of g?

  • \frac{\pi}{3}

  • \pi

  • 2\pi

  • 3\pi

Choose your answer

6
1 mark

The scatterplot shows values of a periodic function space f at integer values of t for 0 less or equal than t less or equal than 10.

Scatterplot showing selected values of a periodic function f for integer values of t from 0 to 10. Points are plotted at (0, 3), (1, 6), (2, 3), (3, 0), (4, 3), (5, 6), (6, 3), (7, 0), (8, 3), (9, 6), and (10, 3). The horizontal axis is labeled t and the vertical axis shows values from 0 to 6.

Based on the values shown, what is the period of space f?

  • 2

  • 4

  • 6

  • 8

Choose your answer