Transcript PreCalc H 5.3 PowerPoint Notes

DO NOW: VERIFY THE X-VALUE
IS A SOLUTION.
2 cos x  1  0 ; x 

3
Pre-Calculus Honors
5.3: Solving Trig Equations
HW: P.373-374 (10, 28, 32, 38, 40,
46, 50, 62, 66)
HOW TO SOLVE A TRIG EQUATION
• Use standard algebraic techniques such as
collecting like terms and factoring.
• Your preliminary goal is to isolate the trig
function.
SOLVE FOR X. 0  x  2
1.) 2 sin x  1  0
What would your solution be
if the domain wasn’t restricted?
SOLVE FOR X. 0  x  2
2.) sin x  2   sin x
Collect Like Terms
FIND ALL SOLUTIONS OF THE EQUATION.
3.) 3 tan x  1  0
2
Extract Square Root
SOLVE FOR X. 0  x  2
4.) cot x cos x  2 cot x
2
Factor
SOLVE FOR X. 0  x  2
5.) 2 sin x  sin x  1  0
2
Factor
SOLVE FOR X.
6.) 2 sin x  3 cos x  3  0
2
Rewrite with a single
trig function: use
identities.
SOLVE FOR X. 0  x  2
7.) cos x  1  sin x
Rewrite with a single
trig function: start by
squaring both sides.
SOLVE FOR X.
8.) 2 cos 3x  1  0
Functions of multiple
angles: solve for 3x first.
FIND ALL SOLUTIONS.
 x
9.) 3 tan    3  0
2
Functions of multiple
angles: solve for x/2
first.
FIND ALL SOLUTIONS.
10.) sec x  2 tan x  4
2
Using inverse.
Pre-Calculus Honors
5.3: Solving Trig Equations
HW: P.373-374 (10, 28, 32, 38, 40,
46, 50, 62, 66)