- University of California, Irvine
- 9 weeks
- 10-12 hours/week
- Paid Certificate Available
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
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.
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.
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.
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.
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)!!!
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.
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.
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.
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.
Sarah Eichhorn and Rachel Lehman
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