In this problem, s denotes the length

| August 30, 2017

Question
1. In this problem, s denotes the length of the arc of a circle of radius r subtended by
the central angle θ. Find the missing quantity. Round answers to three decimal
places, if necessary.
r = 18 meters, θ = 1/2 radian
s=

2. In this problem, A denotes the area of the sector of a circle of radius r formed by the
central angle θ. Find the missing quantity. Round answers to three decimal places, if
necessary.
θ = 1/5 radian, A = 4 square feet

r=

3 .Find the length s and area A. Round answers to three decimal places.

4.Sal’s small slice is 1/6 of a circular 16-inch-diameter pizza and his large slice is 1/8 of a
circular 22-inch-diameter pizza.

Small Slice
$2.30
Large Slice
$3.30
(a) Find the area of the small slice. Give your answer correct to 2 decimal places.
in2
(b) Find the area of the large slice. Give your answer correct to 2 decimal places.
in2
(c) Find how many square inches of pizza you get per dollar when you order the small slice.
Give your answer correct to 2 decimal places.
in2 / dollar
(d) Find how many square inches of pizza you get per dollar when you order the large slice.
Give your answer correct to 2 decimal places.
in2 / dollar
(e) Which size is a better value (i.e. which gives you more pizza for your dollar)?

the small slice

the large slice

the two sizes give you the same amount per dollar

5. In the following problem, t is a real number and P(x,y) is the point on the unit circle that
corresponds to t. Find the exact values of the six trigonometric functions of t.

P(x,y) = (-1/2,

3/2)

sin t =
cos t =
tan t =
csc t =
sec t =
cot t =
6. Find the exact value of each expression. Do not use a calculator.
sin 60° – cos 45°

7. Find the exact value of each expression. Do not use a calculator.
tan 45°cos 60°

8. For each of the following, use fundamental identities to find the values of the
trigonometric functions for the given conditions. Enter the values correct to 2 decimal
places.

(a)
sin θ =
cos θ =
cot θ =

-4/3

sec θ =

0

csc θ =

(b)

cos θ =
tan θ =
cot θ =
sec θ =
csc θ =
9. The point P(-15/17, 8/17) is shown below on the unit circle U corresponding to a real
number t. (Note: The image is not drawn to scale.)

Find the values of the trigonometric functions at t and enter them correct to 3 decimal places.
sin(t) =
cos(t) =
tan(t) =
cot(t) =
sec(t) =
csc(t) =
10. Find the exact value of each of the remaining trigonometric functions of

θ.

cos θ = -4/5, θ in quadrant III
11. Find the approximate value of each of the remaining trigonometric functions of
sin θ = 13/14, θ in quadrant II

θ.

cos

θ=

tan

θ=

csc

θ=

sec

θ=

cot

θ=

12. Use the fact that the trigonometric functions are periodic to find the exact value of this
expression. Do not use a calculator.

0

-1

1

13. Use the even-odd properties to find the exact value of this expression. Do not use a
calculator.
sin(-90°)
0

2

-1

14. Use the even-odd properties to find the exact value of this expression. Do not use a
calculator.
tan(-π)
-1
0
2
15. For each of the following, find the exact value.

(a) sin(2π/3)

Give your answer using the form
A=
B=
(b) cos(150°)

.

Give your answer using the form

.

A=
B=
(c) cos(-60°)

Give your answer using the form

.

A=
B=
(d) tan(5π/6)

Give your answer using the form

.

A=
B=
(e) cot(120°)

Give your answer using the form

.

A=
B=
(f) cot(-150°)

Give your answer using the form

.

A=
B=
(g) sec(2π/3)

Give your answer using the form
A=
B=

.

(h) sec(-π/6)

Give your answer using the form

.

A=
B=
(i) csc(-330°)

Give your answer using the form

.

A=
B=
16. A point on the terminal side of an angle
of the six trigonometric functions of

θ is given. Find the approximate value of each

θ.

(-6, 8)
sin

θ=
cos

θ=

tan

θ=

csc

θ=

sec

θ=

cot

θ=

17. Graph one cycle of the following function.
y=−
1
4
cos

1
3

π
4

x+

State the period, amplitude, phase shift and vertical shift.

period

amplitude

phase shift

vertical shift

18. Graph one cycle of the following function.
y = sin

−x −

π
3

−2

State the period, amplitude, phase shift and vertical shift.

period

amplitude

phase shift

vertical shift

19. Graph one cycle of the following function.
y = 3 sin(−2πx + π)

State the period, amplitude, phase shift and vertical shift.

period

amplitude

phase shift

vertical shift

Graph one cycle of the following function.
y = tan

x−

π
4

State the period.

21. Graph one cycle of the following function.
y = sec

x−

π
4

State the period.

22. Graph one cycle of the following function.
y = −csc

x+

π
6

State the period.

23. Graph one cycle of the following function.
y = cot

x+

π
4

State the period.

24.

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