Unit 2 - Trigonometric Identities and Equations

Unit 2 Review Problems

This document provides a good source of problems to solve in preparation for Test 2. You should also study by re-solving problems from class, past quizzes, and online homework problems. Answers to the problems in this document are provided at the end. On a test, you will earn most of the available points for a given problem by carefully showing the steps taken to reach your answer, rather than for the final answer itself.

You will be provided this list of trigonometric identities (taken from the OpenStax Precalculus textbook to use during the Unit 2 Test, as well as during the Final Exam: Trigonometric Identities 

Unit 2 Learning Objectives:

• Sketch the graphs of tangent, cotangent, secant, and cosecant functions (with at most one transformation); state the domain and range of these functions

• Describe the behavior of the graphs of the tangent, cotangent, secant and cosecant functions near their vertical asymptotes using 'arrow notation'

• Demonstrate an understanding of the connection between the graph of sine or cosine and the corresponding reciprocal function (cosecant or secant)

• State the domain and range of the six inverse trigonometric functions

• Describe the horizontal asymptotes of the inverse tangent function using arrow notation

• Simplify and evaluate compositions of trigonometric functions and inverse trigonometric functions

• Use inverse trigonometric functions to solve for unknown angles in word problems involving right triangles

• Use a provided table of identities to simplify trigonometric expressions and verify new identities

• Use identities to evaluate trigonometric expressions

• Solve various trigonometric equations, including the following approaches:

  • • Use factoring techniques to solve trigonometric equations

    • Solve equations involving a trigonometric function with a change in period

    • Use inverse trigonometric functions to solve an equation

    • Use identities to simplify and solve a trigonometric equation