1. Chapter 5: Trigonometric Functions
Lesson 7: General Solutions to Trigonometric Equations
Mrs. Parziale

2. Vocabulary
General Solutions – a basic way to write an equation for all possible values (infinitely many) without listing all values.

3. Example 1: Solve for all :
Use the calculator. Graph y = sin(x) and y =
Set your window to have x-max of 4
How many solutions. How would you write them all?
Find two key ones – How often do they repeat?

4. Example 1: Solve for all :
General solution are _____________________ or ____________________________

5. Finding the Other Angle Measure
For TRIG(x) = A (i.e. sin(x) = .4199)
Look at A. Determine if it is positive or negative and write down which quadrants your answers will be in.
Take the INVERSETRIG (|A|) and write it down as the ref angle.
Then, calculate the other angle as follows:
Quad II
Quad 1Quad I
Quad III
Quad IV
Write this down

6. Example 2: Solve for all in radians:
General solutions are _____________________ or ____________________________

7. Example 3:
a) Find all values for (x) in radians:

8. Example 3, cont. b) Find all values for  in radians:
Use calculator and write the general solution. Remember, the period of tangent is .

9. Example 3, cont. c) Find all values for  in radians:
Use the unit circle and write the general solution.

10. Example 4:
Find all values for (x) in radians:

11. Closure What is a general solution?
What is added to either a sin or cos function in the general solution?
What is added to the tan function in the general solution?
Solve the following: