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Lesson 20: Trigonometric Equations

Lesson Date: Thursday, April 23rd.

Topic: This lesson covers Chapter 20: Trigonometric Equations.

WeBWorK: There is one WeBWorK assignment on today’s material, due next Thursday 4/30:

Trigonometry – Equations

Question of the Day: If we know , what do we know about the angle ?

#### Lesson NOtes (Notability – pdf):

This .pdf file contains most of the work from the videos in this lesson. It is provided for your reference.

## Basic Trigonometric Equations

#### Equations of the form tan(x)=c

Example 20.1. Solve for : VIDEO: Example 20.1, tan(x)=c

Observation 20.2. To solve , we first determine one solution . Then the general solution is given by: #### EQUATIONS OF THE FORM cos(x)=c

Example 20.4. Solve for : VIDEO: Example 20.4, cos(x)=c

Observation 20.5. To solve , we first determine one solution . Then the general solution is given by: #### EQUATIONS OF THE FORM sin(x)=c

Example 20.7. Solve for : VIDEO: Example 20.7, sin(x)=c

Observation 20.8. To solve , we first determine one solution . Then the general solution is given by: Summary: We summarize the different formulas used to solve the basic trigonometric equations in the following table.

 Solve: Solve: Solve: First, find one solution, that is: . Use: First, find one solution, that is: . Use: First, find one solution, that is: . Use: The general solution is: The general solution is: The general solution is: where where where Example 20.10. Find the general solution of the equation, and state at least distinct solutions.
a) b) ## Equations involving trigonometric functions

Example 20.11. Solve for a) b) c) VIDEO: Example 20.11 – equations with trig functions (linear)

Example 20.12. Solve for .
a) b) VIDEO: Example 20.12 – equations with trig functions (quadratic)