sinθ secθ 1

College Math Survey
Notes 2.2
Mathematician:
9.14.15
PART I – USING THE CHART
Try to fill in the following chart with the information given. Do not look at your notes!

sin 
30
45
60
Ex 1:
cos 
tan 
1
2
1
1
2
3
2
cot 
1
2
sec 
2
3
Use the chart above to decide whether each statement is true or false.
Show work to justify you answer.
a)
sin 30  sin 60  sin 30  60 
b)
cos 60  2cos2 30  1
c)
sin120  sin150  sin 30
csc 
PART II – FINDING REFERENCE ANGLES
Our discussion of 30 o-60 o-90 o and 45 o-45 o-90 o triangles might seem very limited, but in reality
the pattern works for angles that extend way beyond the values just mentioned. The angles of
45o, 30o and 60o simply become the reference angle.
Reference Angle:
The smallest angle that the ____________________ of a given angle makes
with the x-axis.
Ex 2: Given a 300o angle, find its reference angle.
Reference Angle:
This applet helps you understand reference angles better:
http://www.mathopenref.com/reference-angle.html
Ex 3: Find the reference angle for each of the following.
WARNING!!! Before you find the reference angle, find an angle between 0o and 360o (coterminal).
a)
330o
b)
405o
c)
870o
d)
-480o
Ex 4: Find the exact value of each expression – meaning combine reference angles and your
infamous chart from earlier in the week. Do not give decimal answers and watch the signs!
a) sin 870o
b)
cos (-480o)

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