Pre-Calculus: Trigonometry

About this course: This course covers mathematical topics in trigonometry. Trigonometry is the study of triangle angles and lengths, but trigonometric functions have far reaching applications beyond simple studies of triangles. This course is designed to help prepare students to enroll for a first semester course in single variable calculus. Upon completing this course, you will be able to: 1. Evaluate trigonometric functions using the unit circle and right triangle approaches 2. Solve trigonometric equations 3. Verify trigonometric identities 4. Prove and use basic trigonometric identities. 5. Manipulate trigonometric expressions using standard identities 6. Solve right triangles 7. Apply the Law of Sines and the Law of Cosines

Created by:  University of California, Irvine

• Taught by:  Dr. Sarah Eichhorn, Associate Dean, Distance Learning & Tenured Lecturer

• Taught by:  Dr. Rachel Cohen Lehman

Level Intermediate Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.5 stars Average User Rating 4.5See what learners said Coursework

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Syllabus


WEEK 1


Introduction to Trigonometry
In this module, you will get an overview of the course and the foundations of trigonometry. We will also begin exploring angles and different systems for angle measure.


5 videos, 4 readings expand

1. Reading: Syllabus
2. Video: Introduction to Trigonometry
3. Reading: Quiz Notation
4. Reading: Trigonometry Cheat Sheet
5. Reading: Angles and their Measure: Reading and Exercises
6. Video: Converting Between Degrees-Minutes-Seconds and Degrees
7. Video: Converting Between Degrees and Radians
8. Video: Coterminal Angles
9. Video: Reference Angles

Graded: Angles and their Measure

WEEK 2


The Unit Circle and Solving Right Triangles
In this module, we will explore circles and right triangles. We will see several special angles related to particular right triangles and we will learn how to find measurements of sides and angles in right triangles using trigonometric functions.


4 videos, 1 reading expand

1. Reading: Unit Circle and Solving Right Triangles: Reading and Exercises
2. Video: Sketching an Angle in Standard Position
3. Video: Trigonometric Values of Special Angles
4. Video: Right Triangle Trigonometry
5. Video: Right Triangle Word Problems

Graded: Unit Circle and Solving Right Triangles

WEEK 3


Properties of Trigonometric Functions
In this module we will explore several properties of trigonometric functions and discover how to compute values of these functions given information about an angle or a unit circle point.


3 videos, 1 reading expand

1. Reading: Properties of Trigonometric Functions: Reading and Exercises
2. Video: Trigonometric Values Given a Point on the Unit Circle
3. Video: Trigonometric Values Given Information About the Angle, Part 1
4. Video: Trigonometric Values Given Information About the Angle, Part 2

Graded: Properties of Trigonometric Functions

WEEK 4


Inverse Trigonometric Functions
We will now explore the inverse trigonometric functions. These are useful to go backwards - we will seek to find the angles which produce a given value of a trigonometric function.


3 videos, 1 reading expand

1. Reading: Inverse Trigonometric Functions: Reading and Exercises
2. Video: Inverse Trigonometric Values
3. Video: Compositions Involving Inverse Trigonometric Functions, Part 1
4. Video: Compositions Involving Inverse Trigonometric Functions, Part 2

Graded: Inverse Trigonometric Functions

WEEK 5


Basic Trigonometric Identities I



There are several useful trigonometric identities which allow us to simplify trigonometric expressions and find values for the trigonometric functions beyond the special angles. We will begin by exploring the sum and difference identities. Warning: Generally, sin(x+y) does NOT equal sin(x)+sin(y)!!!


4 videos, 1 reading expand

1. Reading: Basic Trigonometric Identities I: Reading and Exercises
2. Video: Verifying Trigonometric Identities
3. Video: Sum and Difference Identities, Part 1
4. Video: Sum and Difference Identities, Part 2
5. Video: Sum and Difference Identities, Part 3

Graded: Basic Trigonometric Identities I

WEEK 6


Basic Trigonometric Identities II
In this module, we continue our exploration of trigonometric function identities. We will begin by learning how to verify such identities. We will then talk about the double-angle and half-angle identities.


4 videos, 1 reading expand

1. Reading: Basic Trigonometric Identities II: Reading and Exercises
2. Video: Verifying Trigonometric Identities- Sum & Difference
3. Video: Verifying Trigonometric Identities - Double Angle Formulas
4. Video: Half Angle Identities, Part 1
5. Video: Half Angle Identities, Part 2

Graded: Quiz: Basic Trigonometric Identities II

WEEK 7


Trigonometric Equations



In this module, we will focus on solving equations involving trigonometric functions. These are usually equations in which the variable appears inside of a trigonometric function and we must use a combination of algebra skills and trigonometry manipulation to solve.


4 videos, 1 reading expand

1. Reading: Trigonometric Equations: Reading and Exercises
2. Video: Solving Trigonometric Equations, Part 1
3. Video: Solving Trigonometric Equations, Part 2
4. Video: Solving Trigonometric Equations, Part 3
5. Video: Solving Trigonometric Equations - Quadratic in Form

Graded: Trigonometric Equations

WEEK 8


Law of Sines and Law of Cosines



The Law of Sines and the Law of Cosines give useful properties of the trigonometry functions that can help us solve for unknown angles and sides in oblique (non-right angle) triangles. We will focus on utilizing those laws in solving triangles, including those which arise in word problems.


6 videos, 1 reading expand

1. Reading: Law of Sines and Law of Cosines: Reading and Exercises
2. Video: Law of Sines and Cosines - ASA Case
3. Video: Law of Sines and Cosines - SAS Case
4. Video: Law of Sines and Cosines - SSA Case
5. Video: Law of Sines and Cosines - SSS Case
6. Video: Law of Sines Word Problem
7. Video: Law of Cosines Word Problem

Graded: Law of Sines and Law of Cosines

WEEK 9


Trigonometry Final Exam
We have completed the new content for the course. In this final module, you will review and practice the topics covered throughout the course. You will end by taking the comprehensive final exam.

Graded: Trigonometry Final Exam