Trigonometry Solving Trig Equations

by: javier

Main Idea What it means to solve

Recall Solving Equations in algebra

Recall Solving Equations in algebra solve x2 + 5x − 6 = 0

Recall Solving Equations in algebra solve x2 + 5x − 6 = 0 (x − 6)(x − 1) = 0

Recall Solving Equations in algebra solve x2 + 5x − 6 = 0 (x − 6)(x − 1) = 0 (x − 6) = 0

(x − 1) = 0

Recall Solving Equations in algebra solve x2 + 5x − 6 = 0 (x − 6)(x − 1) = 0 (x − 6) = 0 x=6

(x − 1) = 0 x=1

Recall Solving Equations in algebra solve x2 + 5x − 6 = 0 (x − 6)(x − 1) = 0 (x − 6) = 0 x=6

these are called conditional equations

(x − 1) = 0 x=1

Main Idea Now Solve Simple Trig Equations

Solving Basic Trig Equations

Solving Basic Trig Equations

solve cos(x) = 0

Solving Basic Trig Equations

solve cos(x) = 0

y 1

x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

solve cos(x) = 0

y 1

x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

Solving Basic Trig Equations

solve cos(x) = −1

Solving Basic Trig Equations

solve cos(x) = −1

y 1

x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

solve cos(x) = −1

y 1

x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

Solving Basic Trig Equations

solve sin(x) = −1

Solving Basic Trig Equations

solve sin(x) = −1

y 1

x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

solve sin(x) = −1

y 1

x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

Solving Basic Trig Equations

solve sin(x) = −1/2

Solving Basic Trig Equations

solve sin(x) = −1/2

y 1

x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

solve sin(x) = −1/2

y 1

x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

Solving Basic Trig Equations

solve tan(x) = 1/2

Solving Basic Trig Equations

solve

y

tan(x) = 1/2

1 x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Solving Basic Trig Equations

solve

y

tan(x) = 1/2

1 x −π 2

−1

π 2

π

3π 2

2π

5π 2

3π

7π 2

Main Idea Now Solve and ALMOST simple Trig Equation

Solving ALMOST Basic Trig Equations

Solving ALMOST Basic Trig Equations solve sin(2x − 45o ) = −1

Solving ALMOST Basic Trig Equations solve sin(2x − 45o ) = −1

Solving OTHER Trig Equations

Solving OTHER Trig Equations solve 2 sin2 (x) + 3 cos(x) − 3 = 0

Solving OTHER Trig Equations solve 2 sin2 (x) + 3 cos(x) − 3 = 0

Solving OTHER Trig Equations

Solving OTHER Trig Equations solve 2 sin2 (x) + 3 cos(x) − 3 = 0

Solving OTHER Trig Equations solve 2 sin2 (x) + 3 cos(x) − 3 = 0

Main Idea Now Solve OTHER Trig Equation

Solving OTHER Trig Equations

Solving OTHER Trig Equations solve sec2 (x) − 2 tan(x) = 4

Solving OTHER Trig Equations solve sec2 (x) − 2 tan(x) = 4

Solving OTHER Trig Equations

Solving OTHER Trig Equations solve 4 sin3 (x) + 2 sin2 (x) − 2 sin(x) − 1 = 0

Solving OTHER Trig Equations solve 4 sin3 (x) + 2 sin2 (x) − 2 sin(x) − 1 = 0