6.7
Trigonometric Equations
The Brightest lesson EVER!!!!
Objectives: Teach some stuff while burning your eyeballs!
Solve Equations Involving a Single Trig Function.
Title: May 5­10:05 AM (1 of 5)
Ex 1
4 cos(θ) ­ 1 = ­3
4 cos(θ) = ­2
cos(θ) = ­1/2
θ = 2π/3 θ = 4π/3
My eyes are bleeding!!
Title: May 5­10:05 AM (2 of 5)
Ex 2
cos(4θ) = ­1
4θ = π + 2kπ We have to add the 2kπ since we are multiplying θ.
θ = π/4 + kπ/2
We need to pick values of k to find what is in our interval from [0 , 2π)
k = ­1
π/4 + ­1π/2 = ­π/4 not in interval
k = 0
π/4 + 0π/2 = π/4
k = 1
π/4 + 1π/2 = 3π/4
k = 2
π/4 + 2π/2 = 5π/4
k = 3
π/4 + 3π/2 = 7π/4
k = 4
π/4 + 4π/2 = 9π/4 not in interval
So θ = π/4, 3π/4, 5π/4, 7π/4
Title: May 5­10:05 AM (3 of 5)
Ex 3
tan(2θ ­ π/4) = ­1
We have to add the kπ since it is tangent & we are multiplying θ.
2θ ­ π/4 = 3π/4 + kπ 2θ ­ π/4 = 7π/4 + kπ
2θ = π + kπ
θ = π/2 + kπ/2
2θ = 2π + kπ
θ = π + kπ/2
We need to pick values of k to find what is in our interval from [0 , 2π)
k = ­1
k = 0
k = 1
k = 2
k = 3
π/2 + ­1π/2 = ­π/2
not in interval
π/2 + 0π/2 = π/2
π/2 + 1π/2 = 2π/2 = π
π/2 + 2π/2 = 3π/2
π/2 + 3π/2 = 4π/2 = 2π not in interval
So θ = π/2, π, 3π/2
Title: May 5­10:05 AM (4 of 5)
Homework:
page 500 (7 ­ 30)
Title: May 5­10:05 AM (5 of 5)