Unit 1 - Fundamentals of Trigonometry

Unit 1 Review Problems

This document provides a good source of problems to solve in preparation for Test 1. 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.

Learning Objectives for Unit 1:

• Convert between radian measure and degree measure

• Identify reference angles and co-terminal angles

• Find the length of an arc on a circle; find the area of a sector of a circle

• Solve problems involving angular and linear velocity, including problems where unit conversions are necessary.

• Be able to evaluate all six trigonometric ratios at familiar angles (i.e. the points on the unit circle) without using a calculator

• Use reference angles to evaluate trigonometric functions

• Given one coordinate of a point on the unit circle, solve for the other coordinate

• Evaluate trigonometric ratios given a point on the terminal side of an angle graphed in standard position

• Identify whether each trigonometric ratio is positive or negative in each of the four quadrants

• Use fundamental trigonometric identities like the Pythagorean identities, quotient and reciprocal identities, cofunction identities, and even and odd properties of the six trigonometric functions, both to evaluate trigonometric functions and to simplify trigonometric expressions

• Solve problems involving right triangles where a trigonometric ratio must be used to find a missing side length

• Graph transformations of the sine and cosine functions, accurately indicating period, midline, amplitude, and phase shift

• Solve applied problems where sine and cosine are used to model periodic phenomena