Hi everyone! Read through the material below, watch the videos, and follow up with your instructor if you have questions.
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: ![]() ![]() | First, find one solution, that is: ![]() ![]() | First, find one solution, that is: ![]() ![]() |
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.