First Semester Review – Math Analysis
Name ___________________
Objective 28: Apply basic trigonometric ratios to solve right triangle problems.
1.
Find the all missing sides and angles: a. b. c.
2.
If csc
 
8
5
, find sin

.
3.
A 14-foot tall ladder leans up against a house. The angle the ladder makes with the ground is 62

. Sketch a picture and determine how far from the ground the ladder touches the building.
Objective 23: Convert decimal degree measures to degree, minutes, and seconds and vice versa.
4.
Change the measure to degrees, minutes, and 5.
Write the measure as a decimal to the nearest seconds. 206.53
. thousandth. 33 10 '6"
Objective 24: Find the number of degrees in a given number of rotations.
6.
Give the angle measure represented by the rotation. a.
6.25 rotations counterclockwise b. 3.1 rotation clockwise
.
Objective 25: Identify angles that are co-terminal with a given angle.
7.
Name 3 angles co-terminal with a) 42° b)
3

5
Objective 27: Use the unit circle to evaluate the circular function .
Objective 81: Determine the location of an arc on the unit circle and find the coordinates of special points on the unit circle.
5

8.
Find the point on the unit circle that corresponds with a)
3 b)

7

6
9.
Evaluate: a.

3
  cos

4
 b. tan
7

6 c. sin
11

3
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First Semester Review – Math Analysis
10.
Determine which quadrant the terminal side of the angle lies in:
7
 a.
6 b.

5

4 c.

5

3
Objective 32: Convert radians to degrees and vice versa.
11.
a. Convert 240

to radians. b. Convert
21

8
to degrees.
Objective #93: Use reference and quadrantal angles to find an angle in standard position.
12.
Given the angle, find the measure of the reference angle: a.
172 ° b.
15

8 b. 293 °
13.
State the measure of the 4 quadrantal angles in radians.
14.
A. Given a reference angle of 52 ° in Quadrant IV, what is the measure of the original angle?
B. Reference angles are always between __________ and __________.
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First Semester Review – Math Analysis
Objective 34: Use the graphs of sine and cosine functions.
Objective 35: Find the amplitude and period of sine and cosine functions.
Objective 36: Write equations of sine and cosine functions given amplitude and period.
Objective 37: Write and graph the equations of sine and cosine functions given vertical and horizontal translations
Objective 38: Model real-world data using sine and cosine functions.
Objective 39: Use amplitude, period and phase shift to graph trigonometric functions.
15.
Problem Amplitude Period Phase Shift Vertical Shift a. b. f ( x )
 
3

4 sin x
 f ( x )

2
 cos x
4
3
4
3
16.
Match the following trigonometric functions with their graphs (tick marks at

2 a. b. b.
b.
Function Graph Period y
 sin x c. d. y
 c.
tan d. y
 sec x y
 cot x e.
f. y
 cos x
on x -axis): y
 csc x
17.
Write an equation of the sine function with amplitude 2, period 5

, phase shift


2
, and vertical shift 3.
Objective 40: Evaluate inverse trig functions.
18.
a.

1 sin 0
c. arccos



2
2

 ________ b. If sin x = .4325, find x. (in degrees) d. arctan 3 _______
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First Semester Review – Math Analysis
Objective 41: Use the trigonometric Identities and concepts to verify other identities.
19.
Simplify: a. csc x
 cos cot x b. cos
2 x tan
2 x
 cos
2 x .
20.
Verify: a.
tan A
 sec csc
A
A b. cos
    
Objective 42: Use sum and difference identities to evaluate expressions.
21.
Use the sum or difference identity for cosine to find the exact value of x a.
cos 75 b. tan 255
22.
What are three different ways you could break down 105° using angle measures on the unit circle.
Objective 43: Solve trigonometric equations.
23.
Solve for real values of x. Write your solution in degrees. a.
sin x
 
1
2 for [0, 2π) b. 3 tan x

3 3 for [0°,180°] c. 2cos x 1 0 for [0, 2π)
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First Semester Review – Math Analysis
Objective 44: Add and subtract vectors geometrically.
Objective 45: Represent vectors using ordered pairs.
Objective 46: Add &subtract vectors and find the magnitude of vectors algebraically.
24.
Write the order pair that represents the vector from C (7, 3) to D ( 2, 1) . Then find the magnitude and direction of the resultant vector.
25.
Let u

1, 4 and v

0,8 . Find each of the following. a. 2 u

3 v b. u v c.
1
2 v
26.
Write vector AB which begins at A if A (2, 7) and B ( 1, 5) .
27.
Find
 u

3
 v if u
 
4, 2 and v

3, 3 . What is the magnitude and direction of the resulting vector?
Objective 47: Find the inner/dot and cross products of vectors.
28.
Find each dot product if x

2, 5 , y

4,1 and z

10, 4 . Are the vectors perpendicular?
How can you tell? a. x y b. x z
Objective 49: Solve problems using vectors and right triangle trigonometry.
29.
Describe the direction of the vector shown. c. y z
30.
Find the horizontal and vertical components of the vector shown.
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First Semester Review – Math Analysis
31. How would you translate the graph of to produce the graph of
32. How would you translate the graph of a. b.
to produce the graph of c. d.
33. How would you translate the graph of
Tell how to translate the graph of
34. y = -0.2(x + 3)
2
– 4
to produce the graph of
in order to produce the graph of the function.
35.
36. How many ways can you name a single polar coordinate?
37. Another name for (-3, 60°) on a polar grid would be?
38. Given the equation r = 3cos2Ө, how many petals does the rose have?
39. Convert (5, 60°) to rectangular coordinates.
40. Convert (3,3) to polar coordinates.
41. Name the graph whose equation is as follows:
a. r = 5Ө b. r = 3 + 3cos2Ө c. r 2 = 3sin2Ө
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First Semester Review – Math Analysis
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