Objectives:
1. To discover and
apply fundamental
trig identities
Assignment:
• P. 309: 27-32 S
• P. 309: 33-42
• P. 311: 73-78
You will be able to discover and
apply fundamental trig identities
Given that sin(35°) = .5736, what is cos(55°)?
Given that sin(35°) = .5736, what is csc(35°)?
Evaluate the following:
sin 60
cos 60
Notice, of course, that the acute angles of a
right triangle are complements.
Also notice that the cofunctions of
complementary angles are equal.
Cofunctions of complementary angles are equal.
sin   cos  90   
cos   sin  90   
tan   cot  90   
cot   tan  90   
sec  csc  90   
csc  sec  90   
*An identity is an equation that is true for all values in the domain.
Cofunctions of complementary angles are equal.


sin   cos    
2



cos   sin    
2



tan   cot    
2



cot   tan    
2



sec   csc    
2



csc   sec    
2

*An identity is an equation that is true for all values in the domain.
Half of the trig functions are reciprocals of the
other half.
1
sin  
csc 
1
cos  
sec 
1
tan  
cot 
1
csc  
sin 
1
sec  
cos 
1
cot  
tan 
Notice that it is not the cofuctions that are
reciprocals: New = Reciprocal of Old. C w/S or T.
Given α and β are complements, csc   5 , and
1
tan   , find each of the following.
2
1. sin α
4. cot α
2. cos β
5. cot β
3. sec β
6. tan β
Given:
x
sin  
z
y
cos  
z
x
tan  
y
Find:
sin 
cos 
Tangent and cotangent are quotients of sine and
cosine.
sin 
tan  
cos 
cos 
cot  
sin 
The following identities are based on the
Pythagorean Theorem.
sin 2   cos 2   1
1  tan 2   sec 2 
1  cot 2   csc2 
Note that sin2 θ = (sin θ)2
Use the right triangle below to prove the
Pythagorean Identities.
Use trig identities to transform the left side of
the equation into the right side of the
equation.
1. 1  cos 1  cos   sin 2 
2.
tan  cot   1
Use trig identities to transform the left side of
the equation into the right side of the
equation.
cos x sin x
sin x

cos x
 sec x csc x
Determine whether the statement is true or
false. Justify your answer.
1.
1  sec2 30  tan 2 30
2.
cos60 csc60  cot 60
Objectives:
1. To discover and
apply fundamental
trig identities
Assignment:
• P. 309: 27-32 S
• P. 309: 33-42
• P. 311: 73-78