Download 8.1 Graphical Solutions to Trig. Equations

8.1 Graphical Solutions to
Trig. Equations
Basic Equation: An equation that involves
a single trig. function set equal to a #.
Cos x = 2
sin x = 1
tan x = 5
Intersection Method:
Ex. 1: Use intersection to find the solution
a) tan x = 3
b) sin x = .5
The X-intercept Method:
1.
2.
3.
4.
5.
Get the equation equal to 0.
Determine the period (p)
Graph the equation over an interval of p.
Find the x-intercepts
For each x-intercept u, all of the #’s
u+kp where k is an integer are solutions
of the equation.
Ex. 2 Solve
a) Sin x = -.75
b) Tan x = 3 sin 2x
Ex. 3 Find all solutions in (0, 2𝜋).
a. Sin x = 0. 238
b. Cos x = 0.873
Ex. 4 Find all solutions in 0° ≤ 𝜃 < 360°
a. Tan 𝜃 = 8.53
b. Cos 𝜃 = −0.35
Complete Hw 8.1 p. 528 {15 – 28}