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Lesson 20: Trigonometric Equations

**Topic**. This lesson covers Chapter 20: Trigonometric Equations.

**WeBWorK**. There is one WeBWorK assignment on today’s material:

`Trigonometry - Equations`

**Lesson Notes**. (download pdf)

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

## Basic Trigonometric Equations

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

**Example 20.1**. Solve for :

**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)*

#### Question

#### Answer

Here is the answer blah.