Advanced Mathematics
Chapter 7 : Trigonometric Functions
Name ______________________________
Date __________________ Period _____
Chapter Test
Show step-by-step work for each problem, or no credit. Write your simplified final answers in the
blanks provided.
1.
2.
3.
a.
Convert 270º to radians. Give the answer in terms of π .
1a.
________________
b.
Convert 192º to radians. Give the answer to the nearest
hundredth.
1b.
________________
a.
Convert
2a.
________________
b.
Convert 2.5 radians to degrees. Give the answer to the
nearest ten minutes or tenth of a degree.
5π
to degrees.
3
2b. ________________
Find two angles, one positive and one negative, that are coterminal with each given angle.
a.
-200º
3a.
___________________________
b.
313.2º
3b.
___________________________
c.
5π
6
3c.
___________________________
d.
142º 10’
3d.
___________________________
4.
A sector of a circle has radius 5 cm and central angle 48º. Find its approximate arc length and
area.
arc length:
___________________________
area:
___________________________
5.
The moon is about 4 x 105 km from Earth, and its apparent
size is about 0.0087 radians. What is the moon’s approximate
diameter?
6.
Find sin θ and cos θ .
5. ___________________
a.
sin θ =
cos θ =
b.
sin θ =
cos θ =
c.
sin θ =
cos θ =
7.
8.
9.
Complete each statement with one of the symbols < , > , or = .
a.
sin 60º __?__ sin 65º
7a.
___________________________
b.
cos 60º __?__ cos 65º
7b. ___________________________
c.
sin 20º __?__ sin 160º
7c.
d.
cos 184º __?__ cos 185º
7d. ___________________________
___________________________
Give the exact value of each expression in simplest radical form.
5π
4
a.
sin
b.
cos (-90º)
8b. ___________________________
c.
sin 150º
8c.
d.
cos
11π
6
8a.
___________________________
___________________________
8d. ___________________________
Give the exact value of each expression or state that the value is undefined.
a.
tan 135º
b.
cot
c.
sec (-60º)
9c.
d.
csc ( −π )
9d. ___________________________
2π
3
9a.
___________________________
9b. ___________________________
___________________________
10.
1
π
where
< x < π , find the values of the
2
3
other five trigonometric functions.
If tan x = −
sin x =
cos x =
csc x =
sec x =
cot x =
11.
12.
Give the exact value of each expression.
a.
Tan −1
b.
1

cot  Sin −1 
2

11b. ___________________________
c.

 3 
sec  Cos −1  −  
 5 

11c. ___________________________
11a. ___________________________
3
Writing: In To obtain the inverse sine function, we restrict the domain of
f ( x ) = sin x to −
π
2
restriction is necessary.
<x<
π
2
. Write a short explanation in which you discuss why this
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