Transcript CLASS 1 CHARACTERISTICS of FUNCTIONS, ALGEBRAICALLY

Chapter 7 – Analytic Trigonometry
7.4 - Basic Trigonometric Equations
Definitions

Trigonometric Equation
An equation that contains trigonometric functions is
called a trigonometric equation.

Basic Trigonometric Equation
Solving any trigonometric equation always reduces to
solving a basic trigonometric equation – an
equation in the form T( ) = c where T is a
trigonometric function and c is a constant.
7.4 - Basic Trigonometric Equations
Solving Basic Trig Equations

The next few examples will show how we can solve
basic trigonometric equations.
7.4 - Basic Trigonometric Equations
Example – pg. 522 # 5
Solve the given equation.
3
sin  
2
This means we want to find the solutions to the
problem above for the following:
 the primary cycle.
 all solutions.
Check by graphing.
Example – pg. 523 #17
Solve the given equation, and list six specific
solutions.
3
cos   
2
Example – pg. 523 # 21
Solve the given equation, and list six specific
solutions.
cos   0.28
Example – pg. 523 # 23

Solve the given equation, and list six specific
solutions.
tan   10
7.4 - Basic Trigonometric Equations
Solving Trigonometric
Equations

In the next example, we will solve a trigonometric
equation that is algebraically equivalent to a basic
trigonometric equation.
7.4 - Basic Trigonometric Equations
Examples – pg. 523

Find all solutions of the given equation.
27.
2 sin   1  0
33. 2 cos   1  0
2
7.4 - Basic Trigonometric Equations
Solving Trig Equations by
Factoring

Factoring is one of the most useful techniques for
solving equations, including trigonometric equations.
The idea is to move all terms to one side of the
equation, factor, and then use the Zero-Product
Property.

The next few examples will cover solving
trigonometric equations by factoring.
7.4 - Basic Trigonometric Equations
Examples – pg. 523

Solve the given equation.
41. 4cos   4cos   1  0
2
53. cos  sin   2cos   0
7.4 - Basic Trigonometric Equations
Try these problems…

Solve the given equation.
48. 2sin 2  5sin   12  0
50. 3 tan 3   tan 


52. sec  2 cos   2  0
54. tan  sin   sin   0
56. 4 cos  sin   3cos   0
7.4 - Basic Trigonometric Equations