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Math 11022 Final Exam Review

The final exam will cover the sections from Trigonometry, 7th edition, Larson - Hostetler, which are listed.

A sampling of exercises is included for practice.

Chapter 1: Trigonometry

1.1 Radian and Degree Measure

Exercises: 9,11,47,79,85,89,93

1.2 Trigonometric Functions: The Unit Circle

Exercises: 3,17,27,33,39,41

Important: Know the unit circle

1.3 Right Triangle Trigonometry

Exercises: 3,11,15,29,37,41,63

1.4 Trigonometric Functions of Any Angle

Exercises: 3,7,13,17,21,33,55,61,81

1.5 Graphs of Sine and Cosine Functions

Exercises: 3,9,13,39,43,45,47,67,69

Important: be able to graph sine and cosine and transformations without a calculator

Given the graph, be able to write the equation for a sine/cosine function

1.6 Graphs of Other Trigonometric Functions

Exercises: 1-6,9,17,21,23

1.7 Inverse Trigonometric Functions

Exercises: 1-15,43-57,61,63,65

Important: Know the domain & range of sin-1, cos-1,

and tan-1 functions

1.8 Applications and Models

Exercises: 5,9,13,17,23

No bearing or harmonic motion applications

Chapter 2: Analytic Trigonometry

2.1 Using Fundamental Identities

Exercises: 57,61,77,81,83

Important: Know the Fundamental Identities on p. 222

2.2 Verifying Trigonometric Identities

Exercises: 5,15,17,25,35,37,47

2.3 Solving Trigonometric Equations

Exercises: 5,13,15,21,29,33,35,37,39

2.4 Sum & Difference Formulas

Exercises: 19,21,23,25,27,33,37,39,41,45,51,57,59

Important: Know the Sum & Difference Formulas on

p. 248

Be able to use the sum & difference formulas to derive the double-angle formulas

2.5 Multiple-Angle & Product-to-Sum Formulas

Exercises: 3,13,19,23,27,35,49,67,75

The formulas in this section will be provided if needed

Chapter 3: Additional Topics in Trigonometry

3.1 Law of Sines

Exercises: 5,9,21,23,27,31,35

Important: Know the Law of Sines and how to use it; be able to find Area of a triangle

3.2 Law of Cosines

Exercises: 5,7,9,15

Important: Know the Law of Cosines and how to use it

The Final Exam consists of 25 short-answer questions and 10 long-answer and graphing problems.

Short-answer problems can be done in a few steps.

Some examples are:

1. Find the exact value in radians:

2. If and , in what quadrant does terminate?

3. Determine the period (or amplitude, or phase shift) for the function

Other examples could include questions on domain/range, fundamental identities, unit circle

Work must be shown and complete solutions given on the long-answer and graphing problems.

Some examples are:

1. Sketch the graph of the function over a two-period interval. Identify the amplitude, period, and phase shift. Label any x-intercepts, maximums, and minimums.

2. Find all exact real solutions, in radians:

3. Verify the identity:

In general, expect

three graphs: 1 sine, 1 cosine, 1 other

1 – 2 identities to verify

1 – 2 trig equations to solve

1 – 2 Right triangle applications

1 Law of Sines/Law of Cosines application

1 Sum/Difference formula application