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