41
TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

Embed Size (px)

Citation preview

Page 1: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 2: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 3: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 4: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Substituted y = 1

Page 5: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 6: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- simplified

Page 7: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 8: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 9: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

** since trigonometry is a cyclical function, we must define our answer further.

Page 10: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 11: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 12: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 13: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

** we will only have to do this when the interval is not already defined

Page 14: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 15: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 16: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Substituted y = 1

Page 17: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Divided both sides by 2

Page 18: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- simplified

Page 19: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 20: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

** no interval was given

Page 21: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 22: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 23: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- factored

Page 24: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Set each factor = 0 and solve

Page 25: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Set each factor = 0 and solve

Page 26: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Take inverse cos of each side…

Page 27: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Take inverse cos of each side…

Page 28: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 29: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Where does cos x = 1 ???

Page 30: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Where does cos x = 1 ???

Page 31: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 32: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 33: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Added 3 to both sides

Page 34: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- divided both sides by 4

Page 35: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- simplified

Page 36: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Square root of both sides

Page 37: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- simplified

Page 38: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

- Inverse of both sides

Page 39: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 40: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.

Page 41: TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using

TRIGONOMETRIC EQUATIONS

Solving a Trigonometric Equation :1. Try to reduce the equation to one involving a single function2. Solve the equation using the same methods as you would an algebraic expression. You might have to factor, square sides, take square roots of both sides, etc.