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Math III Accelerated
Chapter 14
Trigonometric Graphs,
Identities, and Equations
1
Warm Up 14.3
 Identify the trig function equivalent to the
given function.
1
1.
tan 
sin 
3.
cos 
1
2.
sec 
1
4.
csc 
2
14.3 Verify Trigonometric
Identities

Objective:
 Verify trigonometric identities.
3
Reciprocal Identities
 sin θ =
csc θ =
 cos θ =
sec θ =
 tan θ =
cot θ =
4
Trig Identities
 An identity is an equation that is true
for all real values in the domain of the
variable.
5
Quotient Identities
 tan θ =
 cot θ =
6
Pythagorean Identities
 sin2 θ + cos2 θ =
 1 + tan2 θ =
 1 + cot2 θ =
7
Cofunction Identities


sin     
2



csc    
2



cos    
2



sec    
2



tan     
2



cot     
2

8
Negative Angle Identities
Or, “Even/Odd Identities”
 sin (–θ) =
 cos (–θ) =
 tan (–θ) =
9
Example 1
3
3
 Given that cos    and    
,
4
2
find the values of the other 5 trig functions.
10
Checkpoints 1 & 2
 Find the values of the other five trig functions.
1

1. cos   , 0   
4
2
1 3
2. sin    ,
   2
3
2
11
Example 2
 Simplify the expression.
1


sin    
2

 cot 
12
Checkpoint 3
 Simplify the expression.
tan 
3
 sin   tan  csc   cos 
sec 
13
Example 3
 Verify the identity.
1
1  cos 
sec  
 tan  cot  
2
cos 
1  sin 
2
14
Checkpoint 4
 Verify the identity.
cos  x 
2
 sin x
2
cot x
2
15
Homework 14.3
 Practice 14.3
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