Post on 19-Jan-2016
Warm up• If sin θ= and find the exact value of
each function.
1. cos 2θ
2. sin 2θ
3. Use the half-angle identity to find the exact value of the function: cos
5
2
12
5
20
Lesson 7-5 Solving Trigonometric Equations
Objective: To solve trigonometric equations and inequalities
A trigonometric equation is an equation that contains a trigonometric function. For example:
To solve a trig equation, we use algebra to isolate the trig function on one side of the equal sign.
2 2sin cos 1x x 2sin 1 0x 2tan 1 0x
Example
2sin 1 0x
1sin2 x
2
1sin x
If the variable is not restricted there is an infinite number of solutions.
kk 2
6
5,2
6
If principal values are require then only answers in quadrants I and IV work.
306or
Example• Solve
– Use the Pythagorean Identity
• factor the trinomial
0cos2sin33 2 xxxx 22 sin1cos
0)sin1(2sin33 2 xx
0sin22sin33 2 xx
0sin2sin31 2 xx
01sin3sin2 2 xx
0)1)(sin1sin2( xx
2
1sin
01sin2
x
x
1sin
01sin
x
x
6
5
6
orx
2
x
)2,0[
Example• sin x = cos x dividing each side by cos x
produces a different trig function on the left. This is what you want.
• sin2 x= sin x dividing this does not produce a new function. Because you lose the squared term you will miss one of the answers.
x
x
x
x
cos
cos
cos
sin
1tan x
1sinsin
sin
sin
sin 2
xx
x
x
x0)1(sinsin
0sinsin 2
xx
xx
1sin0sin xx