radius of 10 meters. Suppose that in 20 seconds a central angle
of 1/3 radian is swept out. What is the angular speed
ω
of the
object, and what is the linear speed
ν
of the object?
Here give
the exact value of the item followed by its decimal
approximation.
ω
=
ν
=
7. (5 pts.)
If
θ
is an acute angle, and sin(
θ
) = 1/3, obtain
the exact values for the remaining five trigonometric functions.
tan(
θ
) =
cot(
θ
)=
sec(
θ
) =
csc(
θ
)=
cos(
θ
)=
8. (5 pts.)
If the point (4 ,5) is on the terminal side of an
angle
θ
, obtain the exact value of each of the six trigonometric
functions of
θ
.
sin(
θ
) =
cos(
θ
)=
tan(
θ
) =
cot(
θ
)=
sec(
θ
) =
csc(
θ
)=
9. (5 pts.)
What is the reference angle
θ
r
for an angle
θ
= 215°?
θ
r
=
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Page 3 of 4
10. (5 pts.)
Suppose cos
θ
= (3/5) and tan
θ
> 0.
What is the
exact value of each of the remaining trigonometric functions?
sec(
θ
) =
tan(
θ
)=
sin(
θ
) =
csc(
θ
)=
cot(
θ
)=
11. (18 pts.)
Fill in the following table with the information
requested concerning domain, range, and period.
Function Name
Domain
(in radians)
Range
Period
(in radians)
cos(
θ
)
csc(
θ
)
cot(
θ
)
sec(
θ
)
tan(
θ
)
sin(
θ
)
12. (2 pts.)
Use a calculator to obtain the approximate value
of each of the following expressions.
Round your answer to two
decimal places.
sin 20
≈
sin 20°
≈
TEST01a/MAC1114
Page 4 of 4
13. (10 pts.) Carefully sketch y = sin(x) through two periods
that are symmetric about the origin.
Use radian measure and
label carefully.
y
x
14. (10 pts.) Carefully sketch y = sec(x) through two periods
that are symmetric about the origin.
Use radian measure and
label carefully.
y
x
15. (10 pts.) Carefully sketch y = tan(x) through one period.
Use radian measure and label carefully.
y
x
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 Spring '08
 Storfer
 Trigonometry, Tan, pts, Radian

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