MAC 1147 EXAM #2 REVIEW

Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Graph the function.

1) f(x) = -14

(x + 4)2 + 3 1)

Find and simplify the difference quotient f(x + h) - f(x)h

, h 0 for the given function.

2) f(x) = x2 + 5x + 9 2)

Use the graph of the rational function shown to complete the statement.3)

As x + , f(x) ?

3)

1

4)

As x -2-, f(x) ?

4)

List the critical values of the related function. Then solve the inequality.

5) x + 21x + 3

< 3 5)

Find the domain and the vertical asymptote of the function.

6) f(x) = 14

log(x - 5) + 5 6)

Express as a single logarithm and, if possible, simplify.

7) 12

logax + 3 loga y - 2 loga x 7)

Solve the logarithmic equation.8) log5(3x - 4) = 2 8)

The given angle is in standard position. Determine the quadrant in which the angle lies.9) 112° 9)

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.10) r = 4 inches, s = 24 inches 10)

Draw the angle in standard position.

11) 136

11)

Find a positive angle less than 360° or 2 that is coterminal with the given angle.12) -66° 12)

13) -47

13)

Find the length of the arc on a circle of radius r intercepted by a central angle . Round answer to two decimal places.14) r = 10 meters, = 75° 14)

2

Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of thegiven angle. Give an exact answer with a rational denominator.

15) Find cos .

9

2

15)

Use the given triangles to evaluate the expression. Rationalize all denominators.

16) cot3

16)

is an acute angle and sin and cos are given. Use identities to find the indicated value.

17) sin =27

, cos =3 5

7. Find csc . 17)

18) sin = -116

, cos =56

. Find cot . 18)

is an acute angle and sin is given. Use the Pythagorean identity sin2 + cos2 = 1 to find cos .

19) sin =5

319)

Use an identity to find the value of the expression. Do not use a calculator.

20) tan 25° -sin 25°cos 25°

20)

21) tan 25° cot 25° 21)

Find a cofunction with the same value as the given expression.22) sin 76° 22)

3

23) tan 15

23)

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places.

24) cot 10

24)

25) cos 7° 25)

Use a calculator to find the value of the acute angle to the nearest degree.26) tan = 13.2894 26)

Solve the problem.27) A surveyor is measuring the distance across a small lake. He has set up his transit on one

side of the lake 140 feet from a piling that is directly across from a pier on the other side ofthe lake. From his transit, the angle between the piling and the pier is 65°. What is thedistance between the piling and the pier to the nearest foot?

27)

28) A radio transmission tower is 240 feet tall. How long should a guy wire be if it is to beattached 13 feet from the top and is to make an angle of 34° with the ground? Give youranswer to the nearest tenth of a foot.

28)

29) A building 220 feet tall casts a 100 foot long shadow. If a person looks down from the topof the building, what is the measure of the angle between the end of the shadow and thevertical side of the building (to the nearest degree)? (Assume the person's eyes are levelwith the top of the building.)

29)

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function of .30) (-3, -2) Find sec . 30)

Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.31) cos 31)

Find the exact value of the indicated trigonometric function of .

32) csc = -32

, in quadrant III Find cot . 32)

33) cos =2029

, 32

< < 2 Find cot . 33)

Find the reference angle for the given angle.

34) -254

34)

Use reference angles to find the exact value of the expression. Do not use a calculator.

35) sec -54

35)

4

36) sin 32

36)

The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the values of the indicatedtrigonometric function at t.

37) 57

, - 2 67

Find csc t. 37)

Use the unit circle to find the value of the trigonometric function.

38) cot3

38)

Use even and odd properties of the trigonometric functions to find the exact value of the expression.39) sin (-120°) 39)

40) cot -6

40)

41) csc -6

41)

Solve the problem.42) The mean air temperature T, in F°, at Fairbanks, Alaska, on the nth day of the year,

1 n 365, is approximated by: T = 37 sin( 2365

(n - 101)) + 25. Find the temperature at

Fairbanks on day 289, to the nearest tenth.

42)

Use a vertical shift to graph the function.

43) y = 3 cos 3x -2

+ 2 43)

5

44) y = 4 sin 12

x - 2 44)

Determine the amplitude or period as requested.

45) Period of y = 7 sin 5x -2

45)

Determine the phase shift of the function.

46) y = 12

sin (5x + ) 46)

Graph the function.47) y = 4 sin (3 x - 3) 47)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.48) A car is traveling at 34 mph. If its tires have a diameter of 27 inches, how fast are the car's tires

turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.48)

A) 442.28 revolutions per minute B) 846.56 revolutions per minuteC) 423.28 revolutions per minute D) 2659.56 revolutions per minute

6

49) A pick-up truck is fitted with new tires which have a diameter of 41 inches. How fast will thepick-up truck be moving when the wheels are rotating at 280 revolutions per minute? Express theanswer in miles per hour rounded to the nearest whole number.

49)

A) 43 miles per hour B) 17 miles per hourC) 34 miles per hour D) 5 miles per hour

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Graph the function.

50) y = - 14 cos 2x +

450)

51) y = -2 cos (2 x + 3 ) 51)

Solve the problem.52) An experiment in a wind tunnel generates cyclic waves. The following data is collected for

56 seconds:

Time (in seconds)

Wind speed(in feet per second)

0 1914 4328 6742 4356 19

Let V represent the wind speed (velocity) in feet per second and let t represent the time inseconds. Write a sine equation that describes the wave.

52)

7

Graph the function.

53) y = -tan x +2

53)

54) y = 4 cot x +2

54)

Solve the problem.55) The angle of elevation from the top of a house to a plane flying 7200 meters above the

house is x radians. If d represents the horizontal distance, in meters, of the plane from thehouse, express d in terms of a trigonometric function of x.

55)

Graph the function.

56) y = 2 - tan (x +4

) 56)

8

57) y = sec (2x -4

) + 2 57)

58) y = csc (2x +4

) + 1 58)

Find the exact value of the expression, if possible. Do not use a calculator.

59) sin-1 sin 57

59)

60) cos-1 cos 3

60)

Use a sketch to find the exact value of the expression.

61) cos sin-1 35

61)

Using a calculator, solve the following problems. Round your answers to the nearest tenth.62) A boat leaves the entrance of a harbor and travels 72 miles on a bearing of N 20° E. How

many miles north and how many miles east from the harbor has the boat traveled?62)

63) A ship leaves port with a bearing of N 44° W. After traveling 21 miles, the ship then turns90° and travels on a bearing of S 46° W for 6 miles. At that time, what is the bearing of theship from port?

63)

9

Use the given figure to solve the problem.64) Find the bearing from O to D.

50° 55°

33°74°

64)

10

Answer KeyTestname: EXAM #2 REVIEW

1)

2) 2x + h + 53) 04) -5) -3, 6; (- , -3) 6, 6) Domain (5, ); vertical asymptote: x = 5

7) logay3

x3/2

8) 293

9) Quadrant II10) 6 radians11)

12) 294°

13) 107

14) 13.09 meters

15) 2 8585

16) 33

17) 72

18) -5 1111

11

Answer KeyTestname: EXAM #2 REVIEW

19) 23

20) 021) 122) cos 14°

23) cot 1330

24) 3.0825) 0.9926) 86°27) 300 feet28) 405.9 feet29) 24°

30) -133

31) -1

32) 52

33) - 2021

34)4

35) - 236) -1

37) -7 612

38) 33

39) -3

2

40) - 341) -242) 21.5° F43)

12

Answer KeyTestname: EXAM #2 REVIEW

44)

45) 25

46)5

units to the left

47)

48) C49) C50)

13

Answer KeyTestname: EXAM #2 REVIEW

51)

52) V = 24 sin 28

t -2

+ 43

53)

54)

55) d = 7200 cot x

14

Answer KeyTestname: EXAM #2 REVIEW

56)

57)

58)

59)7

60)3

61) 45

62) 67.7 miles north and 24.6 miles east63) N 59.9° W64) S 57° E

15