May 11, 2015
Section 14.4: Solving Trig Equations
Review:
Period of sine and cosine is. . .
Period of tangent is. . .
Solve an equation means. . .
New:
Find the general solutions means there
are an infinite number of solutions. So to find
the answers, you get your answers from the
unit circle on the interval 0 ≤ x ≤ 2π, and then
+2nπ or +nπ
Solve the equation in the interval means
to only find the solutions from the unit circle
over whatever interval they give you (usually,
0 ≤ x ≤ 2π).
Example #1 Find the general solutions for each equation.
2sin x = - √ 3
tan x - 1 = 0
May 11, 2015
Example #2 Find the general solutions for each equation.
sec x - 2 = 0
4sin2 x - 3 = 0
Example #3 Find the general solutions for the equation.
cos x + √ 2 = - cos x
May 11, 2015
Example #4 Solve each equation on the interval 0 ≤ x ≤ 2π
4cos2 x - 1 = 0
sin3 x - 4sin x = 0
Example #5 Solve the equation on the interval 0 ≤ x ≤ 2π
(tan x)(cos2 x) - tan x = 0