MAT & Trig
Notes on 2.1 part 2
Mathematician:
When we filled out the following chart in class yesterday, did you happen to notice any patterns?
(Ignore the fact that sine is the reciprocal of cosecant – we already knew that fun fact!)
Let’s take a look again:

sin 
cos 
30
1
2
3
2
tan 
cot 
1
1
45
1
2
60
sec 
2
3
One helpful hint to filling this out is understanding that tan  
Notice that sin 30o =
csc 
sin 
.
cos 
1
1
. Do you notice another trig function that also has a value of
?
2
2
sin 30o =
= cos 60o = cos (90 – 30o)
tan 60o =
= cot ____o
csc 30o =
=
Does that always happen????
sin 22o =
= cos (90 – 22o) = cos (68o)
Cofunction Identities
For any angle A,
sin A  cos  90  A 
cos A  sin  90  A 
csc A  sec  90  A 
sec A  csc  90  A 
tan A  cot  90  A 
cot A  tan  90  A 
Example 1:
Write each function in terms of its cofunction.
a)
cos 52
b)
tan 71
c)
sec24
Example 2:
Write each function in terms of its cofunction.
a)
cos   40  
b)
cot   10  
MAT & Trig
2.1 Homework – Day 2
1)
Mathematician:
Find the following trig ratios given the 30o-60o-90o triangle drawn below. (Note: This is
what you would do without the chart in front of you!)
sin 300 =
tan 60o =
sec 60o
2)
cos 300 =
=
Find the following trig ratios given the 45o-45o-90o triangle drawn below. (Note: This is
what you would do without the chart in front of you!)
sin 450 =
cot 45o =
sec 45o =
csc 450 =
3) Fill in the following statements.
A)
Sine is a cofunction of
.
B)
Tangent is a cofunction of
.
C)
Secant is a cofunction of
4) Write each function in terms of its cofunction.
A)
tan 36o
B)
cos 20o
C)
sec 54o
D)
sin xo
E)
cot   40o
F)
csc 3  10o



