Download Solving Trigonometric Equations

Pre calculus Problem of the Day
Homework: p. 619 1-57 eoo
Use substitution to determine which of the
given x values are solutions to the equation.
tan x 
3
  2 5 7 4 
, x , ,
,
,
,
3
6 3 3 6 6 3
 7
x ,
6 6


Solving Trigonometric Equations, Finding all Solutions
tan x 
3
3


7
x   2 n or x 
 2 n
6
6
Where n is any integer.

An equivalent answer would be x 


6
 n
Isolate a function to solve a trigonometric equation.
2 cos2 x 1  0
2 cos2 x  1



1
cos x 
2
2


1
2
cos x  
 
2
2
3
5
7
x   2n,
 2n,
 2n,
 2n
4
4
4
 4

Solve a trigonometric equation by factoring.
tan x sin x  sin x
tan x sin x  sin x  0


sin x tan x 1  0
tan x 1  0
sin x  0



x

 2 n
4
5

 2 n
4
x  0  2 n
   2 n
Solving a trigonmetric equation over an interval.
Find all solutions on the interval [ 0, 2¶ ).
sin 4x  

3
sin A  
2
4
A
 2 n
3
4
 4x 
 2n
3
4  2 n
x

12
4

3
2
  5 4  11
x ,
,
,
3 6
3 6

5
or
 2n
3
5
or
 2n
3
5  2 n
or

12
4
5  11 17 23
or
,
,
,
12 12
12
12
Pre calculus Problem of the Day
Homework: p. 619 63 - 83 odds, 85-109 eoo
Solve the following over the interval [ 0, 2¶).
tan 3x  

3
3