1. 5.3 Solving Trigonometric Equations
Turn in your Worksheet on Simplifying Trig Expressions if you haven’t yet.
Objective:
In this lesson you will be learning how to solve trigonometric equations
To solve a trigonometric equation, your goal is to isolate the trigonometric function involved in the equation, then find all values of the variable for which the equation is true.

2. 5.3 Solving Trigonometric Equations
Find all of the solutions of in the interval

3. 5.3 Solving Trigonometric Equations
Solve:
Original equation
Add 1 to each side
Divide each side by 2
But, you were asked to find all solutions, not just those on

4. 5.3 Solving Trigonometric Equations
has the solutions and in the interval
Remember that since has a period of , there are
infinitely many other solutions that can be written as:
and
General solution

5. 5.3 Solving Trigonometric Equations
The equation has infinitely many solutions. Any
angles that are coterminal with are also solutions
to the equation.

6. 5.3 Solving Trigonometric Equations
Solve:
Add 1 to each side
Divide each side by 3
Take the square root of both sides

7. 5.3 Solving Trigonometric Equations You Try:
Solve:

8. 5.3 Solving Trigonometric Equations
Find a general solution:
Set each factor equal to 0

9. Find all solutions in the interval :
5.3 Solving Trigonometric Equations
You Try:
Find all solutions in the interval :

10. 5.3 Solving Trigonometric Equations
Solve: 2 sin2x + 3 cos x – 3 = 0

11. 5.3 Solving Trigonometric Equations You Try:
Solve: 2 sin2x = 2 + cosx on the interval [0,2π).

12. Using Inverse Functions
Find all solutions of sec2x - 2 tan x = 4

13. Exit Ticket
Solve cos2x – cosx = 2 on the interval [0,2π).

14. Homework
Day 1: pg. 364, odd