Important things which we did not have time to cover the last night are highlighted in yellow
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