Chapter 5: Analytic Trigonometry Topic 5: Trigonometric Equations (Day 1)

Chapter 5: Analytic Trigonometry Topic 5: Trigonometric Equations (Day 1)

Exact Values

?

?

?

?/?

?

?

?

Who's Positive Where? What's the reference angle?

Unless otherwise stated, assume all trig equation solutions are ? < ?

General Rules for Solving Trig Equations

Isolate the function to one side of the equation Find a reference angle using the value Decide on quadrants using the +/ Calculate all solutions Example: 2 cos = -1

Factoring As with all factoring: Set the equation to zero, Factor, and Split

Already Factored Example: (tan + 1)(sin - 1) = 0

GCF Factoring Example: tan sin2 = 3 tan

Quadratic Example: 2 cos2 + cos - 1 = 0

You try:

1. 3 sin - 2 = 5 sin - 1

2. sin tan = sin

3. 2 sin2 + 1 = 3 sin

4. 5 sin = 3 sin + 3

5. cos = 2 sin cos 6. (2 cos - 3)(2 sin - 1) 7. cos2 + 2 cos = 3 8. cos2 - 1 = 0

Homework: Textbook Page #19-23, 39-55... ALL ODD

Topic 5: Trigonometric Equations (Day 2) Using Identities to Solve Trig Equations

Some equations will contain more than one function which cannot be separated by factoring. When this is the case, we must look for an identity which will allow us to replace one function with another. The goal is to replace in a way which leaves only ONE trig function in the equation. All solutions must always be checked for extraneous roots Pythagorean Example: 2 sin2 - cos - 1 = 0

Pythagorean Example: sin - cos = 1

`Forward' Example: cos 2 + 3 sin - 2 = 0

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