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
= (1/60) radians/sec.
≈
.0166
radians/sec.
ν
= (1/6) meters/sec.
≈
.166
meters/sec.
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
) = 1/8
1/2
;
cot(
θ
)=8
1/2
;
sec(
θ
) =
3/8
1/2
;
csc(
θ
) = 3;
cos(
θ
)=8
1/2
/3
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
) = 5/(41)
1/2
; cos(
θ
) = 4/(41)
1/2
;
tan(
θ
) =
5/4; cot(
θ
) = 4/5;
sec(
θ
) = (41)
1/2
/4;
csc(
θ
) = (41)
1/2
/5
9. (5 pts.)
What is the reference angle
θ
r
for an angle
θ
= 215°?
θ
r
= 35°
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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
) =
5/3; tan(
θ
) = 4/3; sin(
θ
) = 4/5; csc(
θ
) = 5/4;
cot(
θ
) =
3/4;
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
)
[1,1]
2
π
csc(
θ
)
B, below.
(
∞
,1]
∪
[1,
∞
)
2
π
cot(
θ
)
B, below.
π
sec(
θ
)
A, below.
(
∞
,1]
∪
[1,
∞
)
2
π
tan(
θ
)
A, below.
π
sin(
θ
)
[1,1]
2
π
A={x
ε
:x
≠
(2k + 1)(
π
/2), k any integer }
B={x
ε
:x
≠
k
π
, k any integer }
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
≈
.91
sin 20°
≈
.34
13.,14.,15.:
Partial graphs may be found in the text.
They
generally don’t show two periods that are symmetric with respect
to the origin.
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 Spring '08
 Storfer
 Trigonometry, pts, Radian

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