Download Trig Unit

ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
UNIT TRIG – TRIGONOMETRY
DUE DATE: ______________
Directions: Complete ALL questions for full credit. Do all work on notebook paper
and/or graph paper.
TRIG 1: Right Triangle Trigonometry




Angle of Elevation and Depression Problems
Special Right Triangles
Solve Right Triangles
Write Six Trig Ratios
TRIG 2: Angles of Rotation and Radian Measure



Graph Angles in Standard Position
Complement, Supplement and Coterminal Angles
Convert between radians and degrees
TRIG 3: Evaluating Trigonometric Functions


Express in terms of Reference Angle
Finding Exact Values
TRIG 4: The Unit Circle



Quadrantal Angles
Exact Values of Special Angles
Working Backwards to find Angle
TRIG 5: Graphing Trigonometric Functions




Graphing Trigonometric Functions (Sin and Cos)
Domain, Range, Amplitude, Period, ¼ Period, Axis of Wave
Horizontal and Vertical Shifts
Write Equations from graphs or verbal description
MD/PH/CR/RS 6-15
Page 1 of 6
ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
PROBLEM SET
1)
Find the remaining five trigonometric ratios for  given the following information.
a) sin  = 3/5
2)
b) cos  = 7/12
c) tan  = 9/5
d) csc  = 13/6
Solve each of the following problems. Round to the nearest tenth.
a) A ladder that is 6 meters long leans against a house so that its lower end is 1.5
meters from the building’s base. What angle does the ladder make with the
ground?
b) From the top of the lighthouse 180 feet above the ground, the angle of
depression to a boat at sea is 33. Find the boat’s distance from the foot of the
lighthouse.
c) A vertical pole 30 ft high casts a shadow 18 ft long. What is the angle of
elevation to the sun?
3)
Convert each of the following to radians. No Calculator!
a) 40
4)
c) -120
d) 440
Convert each of the following to degrees. No Calculator!
a)
5)
b) 60
3p
4
b)
11p
6
c)
24p
9
d)
-15p
7
Find the supplement and complement of each of the following angles. No Calculator!
a) 30
MD/PH/CR/RS 6-15
b) 213
c)
3p
7
d)
p
6
Page 2 of 6
ALGEBRA II
6)
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
Find one positive and one negative coterminal angle for each of the
following angles. No Calculator!
7)
c)
5p
d)
-19p
a) 15
b) 421
Given tan  =
(Quadrant IV), determine the value of the five other
12
7
trigonometric functions.
8)
Given csc  = -8 and
trigonometric functions.
9)
p
2
<<
3p
, determine the value of the five other
2
Evaluate each of the following.
a) If tan  = -7/24 in quadrant II, what is cos ?
b) If sec  = 13/5 in quadrant IV, what is sin ?
c) If sin  = -7/11 in quadrant III, what is cot ?
10) Express each of the following in terms of its reference angle.
a)
cos 153
b)
tan 261
e)
tan
f)
sec
i)
cos 4.153R
j)
csc -5.312R
-23p
7
c)
csc 318
d)
sec 571
g)
cot
22p
15
h)
csc
k)
cot 8.137R
l)
sec -7.2R
16p
9
11) Evaluate each of the following. Round answers to ten-thousandths.
a)
d)
sin
13p
7
sec -437
MD/PH/CR/RS 6-15
b)
e)
cot
-28p
11
tan 1.678R
c)
cos 238
f)
csc -9.650R
Page 3 of 6
ALGEBRA II
12)
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
Evaluate each of the following giving exact answers. No Calculator!
a)
cos 120
e)
sec
i)
sin
11p
6
2p
3
b)
sin 150
c)
tan 180
d)
cot 2
f)
sin
g)
csc
17p
4
h)
cos
j)
csc
k)
tan
5p
l)
cos 19
3p
2
19p
3
6
13) Write the equation of each function described.
a)
A sine function has a range of -7  y  7. The function is not reflected and not
shifted. The distance between an intercept and the next consecutive maximum
is 5.
b)
A function has a maximum value of 11 at x = 0. The minimum value is -3. The
horizontal distance between two consecutive minima is 8.
c)
A reflected cosine curve has a maximum value of 3 and a minimum value of -7.
The horizontal between two consecutive intercepts is 9.
14) Identify two equations for each of the functions whose graphs are given below.
A)
B)
MD/PH/CR/RS 6-15
Page 4 of 6
ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
15) Complete the following table.
Amplitude
Reflected?
(Yes or No)
Period
1
4
Period
Horizontal
Shift
Vertical
Shift
Axis of
Wave
a) y = -3 sin 3x + 2
b) y =
1
2
cos
c) y = 2 sin
2p
3
3
2
(x + 4)
(x - p ) - 1
æp
ö
÷
ç x-p÷
è2
ø
d) y + 5 = 6 sin ç
16) Graph more than one cycle of each of the following functions. Be sure to keep scale and label all key values.
a)
y = -4 cos 3x
b)
c)
y = cos  x - 1
d)
MD/PH/CR/RS 6-15
y = - 2 sin
p
x+3
2
y = 2 sin 2x + 3
Page 5 of 6
Range
ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
a)
b)
c)
d)
MD/PH/CR/RS 6-15
Page 6 of 6