FINAL REVIEW - TRIG
2013 FALL SEMESTER AAT(H)
Provide exact simplified answers unless directions state otherwise.
1.
A palm tree needs to be secured. The arborist is going to tie a rope from the tree to a stake in the ground. If the rope is tied 10 feet up on the tree and is to make a 50˚ angle with the ground, how far away from the base of the tree should the rope be staked? How long of a rope should be used?
2.
Height of a highway sign. At a certain time in the afternoon a highway sign casts a shadow that is
136.4 inches long. At the same time, a woman of height 66.2 inches casts a shadow that is 55.5 inches long. How tall is the highway sign to one decimal point?
3.
Given triangle ABC is a right triangle with a right angle at C. Find the tanA if a=6, b=8 and c=10
4.
Given triangle ABC is a right triangle with a right angle at C. Find the sinA, if a = 13, b = 84, and c =
85.
5.
Given triangle ABC is a right triangle with a right angle at C, find the cosA if a=9, b=40 and c=41
6.
Given triangle ABC is a right triangle with a right angle at C. Find the cscA, if a=7, b=24 and c=25
7.
Find the exact value of the sin60˚
8.
Find the exact value of the tan30˚
9.
Find the exact value of the csc150˚
10.
Find the exact value of the sec225˚

11.
Find the exact value of the cot
 4  
 3 
12.
Find the exact values
 a. cos b. sin
4
5

3 c. cot

2
13.
Evaluate the expression exactly a. sin

1
 sin

4 b. sin sin

14.
Evaluate the expression exactly

1


1
3
4

 

1
1
2 
48
55

 d. cot c. cos

1
 cos

6
7

6 e. tan
3

2 d. cos

1
 cos


6
15.
Use a calculator to approximate the sin 52.6° to three decimal places.
16.
Use a calculator to approximate the csc 32.8° to three decimal places.
17.
State in which quadrant or on what axis the terminal side of a 640° angle in standard position lies.
18.
State in which quadrant or on what axis the terminal side of a 90° angle in standard position lies.
19.
State in which quadrant or on what axis the terminal side of a 360° angle in standard position lies.
20.
State in which quadrant or on what axis the terminal side of a –474° angle in standard position lies.
21.
Calculate sinθ if the terminal side of the angle is defined by the line y=-15x, x≥0, and θ is the smallest positive angle in standard position.

22.
Calculate cosθ if the terminal side of  is defined by the line , x 0, and θ is the smallest positive angle in standard position.
23.
Calculate tan  if the terminal side of  is defined by the line , x 0, and θ is the smallest positive angle in standard position.
24.
Calculate the exact value of tanθ if  is in standard position and has a measure of 1845°.
25.
Calculate the exact value of secθ if  is in standard position and has a measure of 1440°.
26.
A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of
θ drawn in standard position. If tanθ = , then what is sinθ?
27.
A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of
θ drawn in standard position. If tanθ =16/30, then what is cosθ?
28.
A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of
θ drawn in standard position. If tanθ =56/33, then what is sinθ?
29.
A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of
θ drawn in standard position. If tanθ = , then what is cosθ?

30.
A right triangle is drawn in QI with one leg on the x-axis and its hypotenuse on the terminal side of
θ drawn in standard position. If sinθ = , then what is tanθ?
31.
Indicate the quadrant in which the terminal side of θ must lie in order for the following to be true: cosθ is positive and sinθ is negative.
32.
Indicate the quadrant in which the terminal side of θ must lie in order for the following to be true: sinθ is positive and tanθ is negative.
33.
Indicate the quadrant in which the terminal side of θ must lie in order for the following to be true: tanθ is positive and cosθ is negative.
34.
If tan  = , and the terminal side of  lies in quadrant II, find sin θ.
35.
If cos  = , and the terminal side of  lies in quadrant I, find sin θ.
36.
If cot θ = , and the terminal side of θ lies in quadrant I, find sec θ.
37.
Evaluate cos(–1260°) – sec(1080°).
38.
Evaluate csc(–2610°) + cos(2880°).
39.
Evaluate tan(45°) cos(90°).
40.
Evaluate csc(–870°) sec(960°).

41.
Convert 401 degrees to radians. Round numbers to two decimal places and leave the answer in terms of π.
42.
Convert
3 
7 radians to degrees. Round the answer to one decimal place.
43.
Convert

3
radians to degrees. Round the answer to one decimal place.
44.
Convert 14.9 radians to degrees. Round the answer to the nearest hundredth of a degree.
45.
Convert 8.2 radians to degrees. Use 3.14 for π and round the answer to the nearest hundredth of a degree.
46.
Convert 65.4° to radians. Round your answer to 3 decimal places.
47.
Convert 194.9° to radians. Round your answer to 3 decimal places
48.
Find the reference angle for in terms of both radians and degrees.
49.
Find the reference angle for
7 
4 in terms of both radians and degrees.

50.
Solve the given triangle and round to one decimal place. b = 180.0 cm.,

= 19.2°,

= 36.4°
51.
Solve the given triangle and round to one decimal place. b = 211.0 ft., c = 52.5 ft.,

= 39.5°
52.
Solve the given triangle and round to one decimal place. b = 29.0 yd.,c = 30.0 yd.,

= 69.0°
53.
Solve the given triangle. Round angle and sides to one decimal place a=37cm, b=122cm, c=130 cm.
54.
Solve the given triangle. Round angle and sides to one decimal place. b = 149 in.,
 = 61.2°, a = 142 in.

The graph at the right models the height of a swing over time (in seconds). When the swing is at rest, the height is zero. Positive heights indicate the height is reached when swinging forward and negative heights indicate the height is reached when swinging backward. Identify the key characteristics of the graph and then write the equation of a sine curve that models this motion.
It is known that photosynthesis (the process by which plants convert carbon dioxide and water into sugar and water) is a Circadian process exhibited by some plants. Assuming that a normal cycle takes 24 hours, the following is a typical graph of photosynthesis for a given plant. Here, photosynthesis is measured in terms of carbon assimilation, the units of which are micromoles of carbon per m 2 /sec. Identify the key characteristics of the graph and then find the equation to model this phenomenon.
Mark Twain sat on the deck of a river steamboat. As the paddle wheel turned, a point on the paddle blade moved so that its distance y, in feet from the water’s surface was a sinusoidal function of time t, in seconds. When Twain’s stopwatch read 4 seconds, the point was at its highest, 16 ft above the water’s surface. The wheel’s diameter was 18 ft, and it completed a revolution every 10 seconds. Draw a graph that models the height of point as a function of time. Identify the key characteristics of the graph. Write an equation to describe the graph.