Precalculus Name:______

Review- Final Exam Review

Date:______

On a separate sheet of paper, answer the following questions, showing all work:

Unit 8: Trigonometric Functions

1)  Find the measure of a central angle q opposite an arc of 5 meters in a circle with a radius of 2.5 meters.

2)  Given a central angle of 30°, find the length of the radius of the circle, to the nearest tenth, whose

intercepted arc has a length of 48 cm.

3)  Given a central angle of 27°, find the length of its intercepted arc in a circle of radius 4 feet to the

nearest tenth.

4)  An arc is 2.3 feet long and is intercepted by a central angle of radians. What is the diameter of the

circle to the nearest tenth?

5)  Through how many radians does a pulley of 6-inch diameter turn when 4 feet of rope is pulled through it

without slippage?

6)  Two gears are interconnected. The smaller gear has a radius of 2 inches, and the larger gear has a radius

of 8 inches. The smaller gear rotates 330°. Through how many radians, to the nearest tenth, does the larger gear rotate?

7)  Find the values of the six trigonometric functions for angle q in standard position if a point with the

coordinates (-9, 12) lies on its terminal side.

8)  A sector has an arc length of 12 feet and a central angle of 2.4 radians.

(a)  Find the radius of the circle.

(b)  Find the area of the sector.

9)  A sector has an area of 17 square inches and a central angle of 0.4 radians.

(a)  Find the radius of the circle to the nearest tenth.

(b)  Find the arc length of the sector to the nearest tenth.

10) A regular octagon is inscribed in a circle with radius of 3 meters. Find the area of the octagon to the

nearest tenth.

11) Find the length of one side of a regular pentagon inscribed in a circle with a radius of 5 inches to the

nearest tenth.

12) Find all solutions for each DABC using the following given information and round to the nearest tenth.

If no solutions exist, write none.

a.  B = 105°, C = 34°, b = 61 yd

b.  A = 48°, C = 71°, b = 33 ft

c.  B = 108°, a = 11 cm, b = 15 cm

d.  A = 92.6°, B = 88.9°, a = 15.2 m

e.  C = 73.4°, a = 144 mm, c = 131 mm

f.  C = 50°, b = 15 in, c = 13 in

Unit 9: Graphs of Trigonometric Functions

Write an equation for the given function given the period, phase shift, and vertical translation:

13) sine function, period = , phase shift = , vertical translation = 6

14) cosine function, period = 10p, phase shift = 5p, vertical translation = -3

15) sine function, period = 2p, phase shift = 0, vertical translation = 4

16) cosine function, period = , phase shift = , vertical translation = 7

17) sine function, period = 8p, phase shift = -p, vertical translation = -5

18) cosine function, period = 4p, phase shift = , vertical translation = -1

19) For each of the given functions, state the amplitude, period, phase shift, and vertical translation, and use

your answers to graph the function within the interval :

20)

21)

22)

23)

24)

25)

Unit 10: Trigonometric Identities & Equations

Verify each of the following identities:

26) / 27) / 28)
29) / 30) / 31)
32) / 33) / 34)

Use the sum or difference identities to find the exact values of each trigonometric expression:

35)

36)

37)

Use the half-angle identities to find the exact values of each trigonometric expression:

38)

39)

40)

Find all solutions of each equation for the given interval:

41)

42)

43)

44)

45)

46)

47)

48)

Unit 11: Vectors & Parametric Equations

49) Find the magnitude of each vector:

a. 

b. 

50) Given the vectors , find each of the following:

(a) 

(b) 

51) Write the ordered pair that represents the vector , given the following coordinates:

a.  A(2, -4) and B(-8, 5)

b.  A(0, 3) and B(7, -1)

52) Lindsay kicks a soccer ball with an initial velocity of 53 ft/sec at an angle of 21° with the horizontal.

(a)  Write parametric equations to represent the path of the soccer ball.

(b)  After 0.5 second, what is the height of the ball to the nearest tenth?

(c)  Find the range of the ball to the nearest hundredth.

53) A sailboat is headed west at 16 mph relative to the water. A current is moving the water north at 5 mph.

(a)  Draw a diagram to represent this situation using vectors.

(b)  What is the angle, to the nearest degree, of the actual path of the sailboat with respect to the current?

(c)  What is the sailboat’s actual speed, to the nearest hundredth, with respect to the ocean floor and the given information?

54) Forces with magnitudes of 35 pounds and 50 pounds act on an object. The angle between the two forces

is 30°.

(a)  Draw a diagram to represent this situation using vectors.

(b)  Using your diagram from part (a), find the magnitude of the resultant of these two forces to the nearest pound.

(c)  Using your answer from part (b) and relative to the 35 pound force, find the direction of the resultant force to the nearest degree.

55) Megan hits golf balls off the practice tee with an initial velocity of 180 ft/sec with four different clubs.

Using each of the following angle measurements made with the different clubs, find how far down the fairway, to the nearest foot, the ball hit the ground:

a.  15°

b.  20°

c.  25°

d.  30°

56) Steve normally swims 2 miles per hour in still water. When he tries to swim directly toward shore at the

beach, his course is altered by the incoming tide. The current is 5 mph and makes an angle of 36° with the direct path to shore. Draw a diagram and use it to find Steve’s resultant speed to the nearest tenth.

57) A toy rocket is launched from level ground at an angle of 82°. It is supposed to release a parachute 375

feet in the air, 5 seconds after liftoff. Find the initial velocity of the toy rocket to the nearest hundredth.

58) Scott practices kicking field goals 30 yd from the goal post with a crossbar of 10 ft high. If he kicks the

ball with an initial velocity of 65 ft/sec at a 45° angle with the horizontal, will Scott make the field goal if the kick is accurate? Explain your answer.

Unit 12: Polar Coordinates & Equations

59) Graph and label each point:

(a) 
(b) 
(c) 
(d) 
(e) 
(f)  /

60) Find the exact rectangular coordinates of each given point:

(a)  / (b)  / (c) 

61) Find the exact polar coordinates of each given point using 0 £ q < 360° and r ³ 0:

(a)  / (b)  / (c) 

62) For each of the following points, find all other polar coordinates for that point, with the restriction -360° £ q £ 360° or -2p £ q £ 2p:

(a)  / (b)  / (c) 

63) Write the given polar equation in rectangular form:

(a)  / (b)  / (c) 

64) Write the given rectangular equation in polar form:

(a)  / (b)  / (c)