AP®MathsCollege BoardPrecalculusExam QuestionsTrigonometric & Polar FunctionsTrigonometric Equations, Inequalities & Identities

Trigonometric Equations, Inequalities & Identities (College Board AP® Precalculus): Exam Questions

11 mins10 questions

Select a download format for Trigonometric Equations, Inequalities & Identities

Scroll for more

Select an answer set to view for
Trigonometric Equations, Inequalities & Identities

1
Sme Calculator
1 mark

The function h is given by h \left(x\right) = 5 \cos \left(2 x\right). Which of the following is an equivalent form for h \left(x\right) ?

  • h \left(x\right) = 10 \cos x \sin x

  • h \left(x\right) = 5 - 10 \sin^{2} x

  • h \left(x\right) = 5 \cos^{2} x + 5 \sin^{2} x

  • h \left(x\right) = \left(5 \cos x\right) \left(5 \sin x\right)

Choose your answer

2
Sme Calculator
1 mark

What are all values of \theta, for 0 \leq \theta < 2 \pi, where 2 \cos^{2} \theta = \cos \theta?

  • \frac{\pi}{3} , \frac{\pi}{2} , \frac{3 \pi}{2} , \text{ and } \frac{5 \pi}{3}

  • \frac{\pi}{2} , \frac{3 \pi}{2} , \frac{2 \pi}{3} , \text{ and } \frac{4 \pi}{3}

  • 0 , \pi , \frac{\pi}{3} , \text{ and } \frac{5 \pi}{3}

  • 0 , \pi , \frac{\pi}{6} , \text{ and } \frac{11 \pi}{6}

Choose your answer

3
Sme Calculator
1 mark

The function f is given by f \left(x\right) = \cos^{2} \left(0.5 x + 0.3\right). The function g is given by g \left(x\right) = f \left(x\right) - 0.5. What are the zeros of g on the interval 0 \leq x \leq 2 \pi ?

  • 0.971 and 4.112

  • 1.494

  • 0.447 and 4.636

  • 2.542

Choose your answer