Download Lesson 4 - Coweta County Schools

Solving a Trigonometric Equation
Find the general solution of the equation.
1. 2cos x  1
2
2
2
1
cos x 
2
2
cos x  
2
2

2

x  cos  

2


1
 3
x ,
4 4
 n
x 
4 2
 

4 4

4

4

4
Solving a Trigonometric Equation
Find the general solution of the equation.
2. 7tan x  9  2
7tan x  7
7
7
tan x  1
x  tan  1
1
3 7
x
,
4 4
3
 n
x
4
 

4 4
2 

4

4
Solving a Trigonometric Equation
Find the general solution of the equation.
 5
x ,
3. cot x  1  2
6 6
2
cot x  3
5

,

n

x


n

cot x   3
6
6
3
tan x  
 


3
6
6 6


3

1

x  tan  
6
6
3


2
Solving a Trigonometric Equation
Find the general solution of the equation.
4. 2cos x  3
2
2
3
cos x 
2
 11
x ,
6 6
11

 2n
x   2n ,
6
6
 3

x  cos 
 2 

1
2 

6
6

6
Solving a Trigonometric Equation
Find the general solution of the equation.
5. cot x  1  0
cot x  1
tan x  1
x  tan  1
1
3 7
x
,
4 4
3
 n
x
4
 

4 4
2 

4

4
Solving a Trigonometric Equation
Find the general solution of the equation.
6. 4sin x  3  0
2
4 sin x  3
4
4
3
2
sin x 
x
2

3

x  sin  
 2 
1
,
3 3
2
 n
x   n ,
3
3

4
3
sin x  
2
 2

 

3 3

3

3
3
Factoring to Solve a Trigonometric Equation
Solve the equation in the interval 0 < x < 2.
7. sin x  sin x  0
2
sin x sin x  1  0
sin x  0 sin x  1
x  0 , x 

2
Factoring to Solve a Trigonometric Equation
Solve the equation in the interval 0 < x < 2.
8. 3 sinx  2 sin x cos x
3 sinx  2 sin x cos x  0
sin x 3  2 cos x   0
2 cos x  3
3
sin x  0 cos x 
2
 11
x  0 , x 
6
,
6

2 

6
6

6
Factoring to Solve a Trigonometric Equation
Solve the equation in the interval 0 < x < 2.
9. cosx  1sinx  1  0
cos x  1
x0
sin x  1
x

2
Factoring to Solve a Trigonometric Equation
Solve the equation in the interval 0 < x < 2.
10. tan x sec x  2 tan x
tan x sec x  2 tan x  0
tan xsec x  2   0
sec x  2
2
tan x  0 cos x 
2
 7
,
x0
x
4
,
4

2 

4
4

4
Factoring to Solve a Trigonometric Equation
Solve the equation in the interval 0 < x < 2.
11. sin x tan x  sin x
sin x tan x  sin x  0
sin x tan x  1   0
sin x  0 tan x  1
 5
x  0 , x  ,
4 4


4

4

4
Factoring to Solve a Trigonometric Equation
Solve the equation in the interval 0 < x < 2.
12. tan x  tan x  0
2
tan x 1  tan x   0
tan x  0 tan x  1
3 7
x  0 ,
x
4
,
4


4
2 

4

4

4
Using the Quadratic Formula
Solve the equation in the interval 0 < x < .
13. 2sin x  sin x  3  0
2
2 sin x  3sin x
1   0
2 sin x  3 sin x  1

3
x
sin x  
2
2
Using the Quadratic Formula
Solve the equation in the interval 0 < x < .
14. 2 tan x  3 tan x  1  0
2
 9  4 2  1
3
tan x 
4
3  9  8 3  17  1.781
tan x 

 0.281
4
4
1
1
x  tan 1.781 x  tan  0.281  0.274
  0.274 x  2.87
x  1.06
Using the Quadratic Formula
Solve the equation in the interval 0 < x < .
15. 5cos x  3cos x  2
2
5 cos x  3cos x  2  0
2
 9  4 5 2 

3
cos x 
10
 3  9  40  3  49  0.4

cos x 
 1
10
10
1
1
x  cos  1
x  cos 0.4
x  1.16
x 
Using the Quadratic Formula
Solve the equation in the interval 0 < x < .
16. cos x  4 cos x  2
2
cos x  4 cos x  2  0
2
4  16  4 1 2
cos x 
2
4  16  8
4  8  3.414
cos x 

 0.586
2
2
1
x  cos 0.586
x  0.945