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Unformatted text preview: Student: Shanna Hawxhurst
Date: 3f17109 Instructor: Christine Curley Course: 903 CURLEY C, MAT 200 004 016 Assignment: Week 10, Sections 6.16.6 Time: 6:49 PM Book: Strayer University Math 200:
Precalculus
1. Find the six trigonometric function values of the speciﬁed angle. I 40
sm B= — (Simplify your answer 8 9
cos = —
41 (Simplify your answer tat)—ﬂ
1‘1—9 (Simplify your answer 41
sec B= — (Simplify your answer 3. . B =
csc 40 (Simplify your answer 9 tB= —
CO 40 (Simplify your answer csc9= 1.2 sin 9 as .83 cos B as .55 . Type an integer or a fraction.) . Type an integer or a fraction.) . Type an integer or a fraction.) . Type an integer or a fraction.) . Type an integer or a fraction.) . Type an integer or a fraction.) tan Bra 1.51 (Round to 2 decimal places.) sec Bra 1.81 cot 9:: .66 (Round to 2 decimal places.) Page 1 40 Given a function value of an acute angle, ﬁnd the other ﬁve trigonometric function values. Student: Shanna Havvxhurst
Date: 3f17109
Time: 6:49 PM Instructor: Christine Curley
Course: 903 CURLEY C, MAT 200 004 016
Book: Strayer University Math 200: Assignment: Week 10, Sections 6.16.6 Lu 4_ A baseball diamond is a square 90 ft on a side. Ifa
line is drawn from third base to a runner between
home plate and ﬁrst base, then a right triangle QPH P h
is formed where [QPH is 25°. Q
Using a trigonometric ﬁinction, ﬁnd the distance 90 ﬂ
from third base to the runner. The runner is 99.3 H
feet from third base.
(Round to 2 decimal places.)
5_ Convert the following angle to decimal degrees. The answer in decimal degrees is — 24.42 °.
(Round to four decimal places.)
— 24°25'12"
(1 Convert the following angle to decimal degrees. The answer in decimal degrees is — 75.5458 °.
(Round to four decimal places.)
 ?5°32'45"
1 Convert the following angle to Enter the components of the converted angle.
degreesminutogseconds.
30 ° 32 ' 2 "
30.534°    x »
(Slmphty your answers. Type an integer or dec1mal.
Round to the nearest whole number of seconds.)
8_ Convert the following angle to The answer is 22 0 42 ' 7 "I Precalculus Find the exact values of csc 60°, sec 60°, and cot 60°. 2V3— csc 60°= —
3 (Simplify your answer. Type an integer or a fraction. Type an exact answer. using radicals as needed. Rationalize any denominators.) sec 60°: 2 (Simplify your answer. Type an integer or a fraction. Type an exact answer, using radicals as needed. Rationalize any denominators.) V? cot 60°= —
3 (Simplify your answer. Type an integer or a fraction. Type an exact answer, using radicals as needed. Rationalize any denominators.) degrees—minutes—seconds. u=22.?02° Page 2 (Simplify your answers. Type an integer or a
decimal. Round to the nearest whole number of
seconds.) Student: Shanna Hawxhurst Date: 3(17109 Time: 6:49 PM Instructor: Christine Curley
Course: 903 CURLEY C, MAT 200 004 016
Book: Strayer University Math 200: Precalculus Assignment: Week 10, Sections 6.16.6 9. 10. 11. Use a calculator to ﬁnd a decimal approximation for the values of the following trigonometric functions. sin 38°24', cos 38°24', tan 38°24' sin 38°24' = .6211478
(Simplify your answer. Type an integer or a decimal. Round to seven decimal places if needed.) cos 38°24' = 3836935
(Simplify your answer. Type an integer or a decimal. Round to seven decimal places if needed.) tan 38°24'= .7925902
(Simplify your answer. Type an integer or a decimal. Round to seven decimal places if needed.) Find the values of the following trigonometric ftulctions. sin 36°. cos 36°, tan 36° sin 36°= .5878
(Round to four decimal places.) cos 36°= .809
(Round to four decimal places.) tan 36°= .7265
(Round to four decimal places.) Use the table feature of a grapher to ﬁnd the acute angle 9. to the nearest tenth of a degree. for the given
ﬁJnction value. tan 0 = 0.9055 0 = 42.2
(Round to the nearest tenth ofa degree.) Use the table feature ofa grapher to ﬁnd the acute angle 9, to the nearest tenth ofa degree, for the given
function value. cot B = 2.2512 9: (Round to the nearest tenth of a degree.) Page 3 Student: Shanna Hawxhurst Date: 3(17109 Time: 6:49 PM Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Course: 903 CURLEY C, MAT 200 004 016 Precalculus Book: Strayer University Math 200: 14. 16. Rewrite sec 62° in terms of a(n) 23° angle and in terms of the reciprocal ofa trigonometric function. sec 67°: 1 23° Given that sin 51°= 0.7?7] cos 51°= 0.6293
tan 5 °= 1.2349 cot 5 °=0.8098
sec 51°: 1.5890 csc 51°= 1.2868 ﬁnd the six ﬁlnction values of 39°. sin 39°= .6293 cos 39° = .7771
(Round to 4 decimal places.) cot 39°: 1.2349 sec 39°= 1.2868
(Round 4 decimal places.) Solve the right triangle shown, where
a=6.1 and CL=15.5°. Find the measure of angle 24.5 °
(Round to the nearest tenth as needed.) Find the length of side b. D (Round to the nearest tenth as needed.) Find the length of side c. D (Round to the nearest tenth as needed.) Solve the right triangle ABC, with C = 90°. A=21° 24',c= 11.6ft tan 39°= .8098 Page 4 csc 39° = 1.5890 In the right triangle ABC, with C = 90°, B = ° '. (Simplify your answers. Type an integer or a
decimal.) The length of side a = D it and ot‘side b = D it. (Simplify your answers. Type an integer or a
decimal. Round to the nearest tenth if needed.) Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Date: 3/17/09 Course: 903 CURLEY C, MAT 200 004 016
Time: 6:49 PM Back: Strayer University Math 200:
Precalculus
11 A marketing company wants to set up an easel to display posters advertising their latest products. The top of the easel is to be 6 feet high with the back flush against the wall. They want the angle between the front
and back legs of the easel to be 23°. How far from the wall should the front legs be placed in order to
obtain this angle. The distance between the front and back legs should be 2.5 feet.
(Round to the nearest tenth.) 18_ From a hot air balloon 4 km high, a person looks
east and sees one town with angle of depression of
11°. He then looks west to see another town with
angle of depression of 84°. The distance between the two towns is km.
(Round to the nearest tenth.) 19_ For the angle, state in which quadrant the terminal
side lies. 12°18‘ The angle is in Quadrant (Type your answer as I, 11, III. or IV.) 20. PDT an angle 0f the fOHUWlﬂg measures State in The terminal side of — 188° lies in quadrant II .
which quadrant the terminal side lies. (Type I, “I “L 0]. IV)
— 188° 21_ Determine whether angles with the following Are the given angles coterminal'?
measures are coterminal. No v Yes 20° and 1 100° 22_ Find the complement and supplement of T8.09°.
The complement is 11.91 °.
The supplement is 101.91 °. 23 Find the complement and supplement of 72.1 1°. The complement is 17.89 °. The supplement is l0?.89 °. Page 5 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Date: 3/17/09 Course: 903 CURLEY C, MAT 200 004 016
Time: 6:49 PM Book: Strayer University Math 200:
Preealculus 24_ Assume that a is an angle in standard position whose terminal side contains the point
(— 2E. 4). Find the exact values of the following functions. sin a = 050$: Page 6 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Date: 3/17109 Course: 903 CURLEY C, MAT 200 004 016
Time: 6:49 PM Book: Strayer University Math 200:
Precalculus
25_ A function value and a quadrant are given. Find the other ﬁve function values. Give exact answers. cot B = 4 , Quadrant III V17 ~4'UI7‘ I
8111 9 cos B w an 9 4 ‘
csc9= ~\ll7 sec9= —— — l
YOU ANSWERED: —
ll 17
—_4
V 17
1?
T?
17
 4V 1?
26. Find the reference angle and the exact function value.
sin "£425"
The reference angle is °.
sin 7425° = D
27’. Find the exact value of csc (90°).
csc (90°) = 1 (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any
numbers in the expression. Type N ifthe answer is undefined.) 23 Find the reference angle and the exact value of the
tangent, if it exists. tan( 120°) What is the reference angle? D" What is tan(120°)? : {Type N it‘lhe value is undeﬁned.) Page 7 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Date: 3/17109 Course: 903 CURLEY C, MAT 200 004 016 Time: 6:49 PM Book: Strayer University Math 200:
Precalculus 29_ Find the signs of the six trigonometric ﬁrnction values for the given angle.
30
sin 3° is D, cos 3° is and tan 3° is (Type P for positive or N for negative.) csc 3° is sec 3° is and cot 3° is (Type P for positive or N for negative.) 30. Find the signs of the six trigonometric function
values for the given angle.
 69°
sin — 69° is N , cos — 69° is P , and tan — 69° is N.
(Type P for positive or N for negative.)
csc —69° is N . sec — 69° is P , and cot — 69° is N.
(Type P for positive or N for negative.)
31_ Given that sin 33° = 0.5446. cos 33° = 0.8382, and
tan 33° = 0.6494, ﬁnd the trigonometric function
values for 327°.
sin 327°= — .5446
(Round to Four decimal places.)
cos 327°= .8387
(Round to four decimal places.)
tan 32'?°= — .6494
(Round to four decimal places.)
32_ An airplane ﬂies 120 kilometers from an airport in a direction of 220°. How far west of the airport is the
airplane then? How far south? In navigation,
directions are given in degrees measured clockwise
from north. The airplane is kilometers west. (Round to the nearest integer.) The airplane is kilometers south. (Round to the nearest integer.) Page 8 Student: Shanna Hawxhurst Date: 3/17/09 Time: 6:49 PM L14
L44 Instructor: Christine Curley
Course: 903 CURLEY C, MAT 200 004 016
Book: Strayer University Math 200: Precalculus Find the function value. tan 29] .2" tan 291.2° a:  2.5782
(Round to four decimal places.) Find the function value. sin 111°36’ Sin “1036193 .9298
(Round to four decimal places.) Given that cos B = 0.3584 and 270° < B < 360°, ﬁnd 9. e = D° (Round to the nearest integer.) Given that sin 9: — 0.95] l and 220° < 9 < 360°. find 9.
B= 288 ° (Round to the nearest integer.) 51':
Which of the unit circles has a point determined by T? 52':
Choose the unit circle with a point determined by YOU Ah SWERED: C Page 9 Assignment: Week 10, Sections 6.16.6 Student: Shanna Hawxhurst
Date: $17109 Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Course: 903 CURLEY C, MAT 200 004 016 Time: 6:49 PM Book: Strayer University Math 200:
Precalculus
33 Find two real numbers between  2n: and 231 that La
\0 40. 41. 42. determine the point indicated on the unit circle. Two real numbers that determine the indicated point are — n: —111'E 6’6 (Simplify your answers. Type fractions with n: in the numerator. Use a comma to separate answers.) Determine whether angles with the following
measures are coterminal. Determine whether angles with the following
measures are coterminal. Convert the following degree measure to radian
measure. 55° Convert the following degree measure to radian
measure. 660° Convert the following degree measure to radian
measure. 64.22" Page 10 Are the angles coterrninal'.’
(:3 No CD Yes Are the angles coterrninal'.’ '9' No Yes
117: _
55°= — radlans
36 (Type a simpliﬁed fraction. Type an exact answer in
terms of 1c.) _ 0: 11a _
660 —3 radians (Simplify your answer. Type an integer
or a fraction. Type an exact answer in terms of 11:.) 64.22°= 1.121 radians (Type an integer or a decimal. Round to the nearest
thousandth as needed.) Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Date: 3/17/09 Course: 903 CURLEY C, MAT 200 004 016
Time: 6:49 PM Book: Strayer University Math 200:
Precalculus
44_ Convert the following radian measure to degree measure. Use the calculator value for 31.
I la
— — rad
5 Ha — Trad= 396 degrees (Round to the nearest thousandth.) 45_ Complete the table.
Distance, 5 (Arc length) Radius, r Angle, 9
6 ft 1
s—ﬁ D
4
150 cm D m 45° (Round to the nearest hundredth as needed.) 46_ In a circle of radius 80 cm, an arc 172 cm long subtends an angle of how many radians? How many
degrees? 43
The are subtends an angle of E radians. (Simplify your answer. Type a fraction.) The are subtends an angle of 123 degrees.
(Round to the nearest degree.) 41 A printing press has a roller l6 inches in diameter. The speed ofa point on the roller's surface moves at 98
feet per second. What is the roller's angular speed? The angular speed of the roller is 14? per second.
(Round to the nearest tenth as needed.) 48_ A water wheel has a radius of 12 ft. A river passing through the water wheel turns the wheel at 1 l
revolutions per minute (rpm). What is the speed of the river in miles per hour? The river's speed is approximately 1 mph.
(Round to the nearest hundredth.) Page 11 Student: Shanna Hawxhurst Date: 3(17109 Instructor: Christine Curley
Course: 903 CURLEY C, MAT 200 004 016 Assignment: Week 10, Sections 6.16.6 Time: 6:49 PM Book: Strayer University Math 200:
Precalculus
4C)_ The following point is on the unit circle. Find the coordinates of its reﬂection across the xaxis. the yaxis. and the origin. l ‘5) The reﬂection across the xaxis is [ — 2 3 _ 9 3 ii]
3’ 3 ' (Type an ordered pair. Type an integer or a fraction. Type exact answers for each coordinate, using radicals
as needed.) 2
The reﬂection across the yaxis is [;, — 3
(Type an ordered pair. Type an integer or a fraction. Type exact answers for each coordinate, using radians
as needed.) 2V5— The reflection across the origin is . (Type an ordered pair. Type an integer or a fraction. Type exact answers for each coordinate, using radicals
as needed.) \f3— rt 1
The number — determines a point on the unit circle with coordinates [— —]. What are the coordinates 6 2 i 2
I y a
of the pomt determmed by — E?
III
The coordinates of the point determined by — E are (Type an ordered pair. Type an integer or a fraction. Type exact answers for each coordinate, using radicals
as needed.) Find the function value using coordinates of points on the unit circle. Give the exact answer. mg] vr (Type an exact answer. using radicals as needed. Rationalize the denominator, ifnecessary.) Page 12 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Date: 3/17109 Course: 903 CURLEY C, MAT 200 004 016
Time: 6:49 PM Book: Strayer University Math 200:
Precalculus
52_ Find the exact value of the following expression. Do not use a calculator to enter a decimal approximation.
cos it
cos it = (Type an integer or a fraction. Type an exact answer, using radicals as needed.) 53 Use the unit circle, along with the deﬁnitions of the _ 1: TE 11:
circular functions, to ﬁnd the exact values for the 5m 3 C05 ? ta" ?
given functions. Then ﬁnd the values on your
calculator (in radian mode). 113 TE n ‘
sin —= .8660 cos —= .5 tan —= V3—
3 3 3
(Simplify your answers. Rationalize the denominators. Type exact values.)
II: 1: :t
sin —=s .8660 cos —ra .5 tan —=s 1.?321
3 3 3
(Round to four decimal places.)
YOU ANSWERED: .8
54_ In which quadrant is tangent positive?
Choose the correct answer.
V I, III : III, IV
III I
55_ Determine the amplitude and phase shift of the function y = — 3SIII(X). Also, choose its graph. The amplitude is 3 . The phase shift is 0 . Choose the correct graph below. 9.
A}: A? A)”
10: 10: 10:
I I: X E X E \
Eflrféhjédg—* ﬁgﬂhgﬂ$ﬁfﬁh_’ rrrrrtnnnan—*
— _ 0 1 _ 10 ~W\/‘1~0
v10: —1o£ '10: Page 13 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Date: 3/17109 Course: 903 CURLEY C, MAT 200 004 016
Time: 6:49 PM Book: Strayer University Math 200:
Precalculus
56. . _ . . 1"
Determlne the amplltude, penod, and phase shift ofy = — 3cos[x — 1:
The amplitude is 3 . The period is 27: . The phase shift is 3 .
57'. . . . . 1‘
Determlne the amphtude, period, and phase shift of y = 2 sin + II].
The amplitude is 2 . The period is 8 . The phase shift is — 4 .
58_ Write an equation of the form 10}?
y = A sin (B[x  C]) + D whose graph is the given —
sine wave.
Choose the correct answer below.
CJA II:
y=3sm 2 x— +1
F IB 3 . II: 1
= sm x  — 
y 4 . . . .
QC. _ . n i ?
y_3SIn2X_4 _l DD” 3 H 1 H 079 it 157 3“ 236
=' ——+ —s..;—s.;—s
y 5'“ x 4 4 2 4
59, Graph, using addition of ordinates. y=sin X +cos 3X Choose the correct graph below. Q.
A)’
5_
.. .i x
ﬁg .353: 31:35.52
.__5__ Page 14 Student: Shanna Havmhucrst Instructor: Christine Curley Assignment: Week 10, Sections 6.16.6 Date: 3/17/09 Course: 903 CURLEY C, MAT 200 004 016
Time: 6:49 PM Book: Strayer University Math 200:
Preealculus 60_ Graph, using addition of ordinates. y =4cos x +sin 5): Choose the correct graph below. Page 15 ...
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