Unit 6 Test 2 Review Writing equations from graphs.
y  Asin[ B( x  C )]  D
A
max  min
2
Name ____________________
B
2
period
or
B
360
period
D
max  min
2
A represents the amplitude of the graph. The amplitude is the vertical distance from the horizontal axis of the graph to the
maximum value or the minimum value of the graph. The amplitude is also equal to half of the difference between the
maximum and minimum values.
B represents the angular frequency of the graph. The angular frequency describes how many crests or troughs of the graph
are present within a 360°or 2π portion of the domain of the graph. The angular frequency is also found by dividing 2π by
the period, which is the horizontal distance between two consecutive maximum or minimum values.
C represents the phase shift, or horizontal translation of a sine function.
D represents a vertical translation of the graph. The line y = D is the equation of the sinusoidal axis, which is the
horizontal line representing the distance that is midway between the crests and troughs of the graph.
Graph 1
1. If there is no horizontal shift then this graph is best described as
Positive Sine
Negative Sine
Positive Cosine
Negative Cosine
2. What is the maximum and minimum value of the function?
Max __________
Min ____________
3. What is the amplitude? A = ___________
4. What is the vertical displacement? D = ____________
5. How long is a period? ________________
6. Calculate B using degrees.
7. Write the equation of the graph
Graph 2
1. If there is no horizontal shift then this graph is best described as
Positive Sine
Negative Sine
Positive Cosine
Negative Cosine
2. What is the maximum and minimum value of the function?
Max __________
Min ____________
3. What is the amplitude? A = ___________
4. What is the vertical displacement? D = ____________
5. How long is a period? ________________
6. Calculate B using degrees.
7. Write the equation of the graph
Graph 3
A = __________
B = __________
D = __________
Equation________________
Graph 4
A = __________
B = __________
D = __________
Equation________________
Graph 5
A = __________
B = __________
D = __________
Equation________________
Graph 6
A = __________
B = __________
D = __________
Equation________________
2. Fill in the blank to complete the sentence below.
One _____ is the measure of a central angle that intercepts an
arc equal to the radius of the circle.
A) coterminal B) radian C) degree D) supplementary E)
complementary
3. Determine a pair of angles (one positive and one
negative) in degree measure coterminal
to the angle 73°.
A) 253° , –107°
D) 146° , −73°
B) 433° , –287°
E) 253° , –287°
C) 373° , –227°
4.
5. Describe the relationship between f (x) = cos(x) and
g(x) = cos7x – 11. Consider amplitude, period, and
shifts.
6.
A) The period of g(x) is seven times the period of f(x).
Graph of g(x) is shifted downward 11 unit(s) relative to
the graph of f(x).
B) The amplitude of g(x) is seven times the amplitude
of f(x). Graph of g(x) is shifted downward 11 unit(s)
relative to the graph of f(x).
C) The period of g(x) is seven times the period of f(x).
Graph of g(x) is shifted upward 11 unit(s) relative to
the graph of f(x).
D) The amplitude of g(x) is seven times the amplitude
of f(x). Graph of g(x) is shifted upward 11 unit(s)
relative to the graph of f(x).
E) The period of g(x) is eleven times the period of f(x).
Graph of g(x) is shifted downward 7 unit(s) relative to
the graph of f(x).
9. Find a and d for the function f (x) = a sin x + d such
that the graph of f (x) matches the graph below.
12.
7.
8.
10.
11. Find the reference angle for the angle –52°.
A) 412°
B) 142°
C) 52°
D) –52°
E) –142°
13.
14. Define one degree.
A) One degree is one three hundred and sixtieth of a circle.
B) One degree is one sixth of a circle.
C) One degree is the measure of a central angle that intercepts an arc equal in length to the radius of the circle.
D) One degree is the measure of a central angle that intercepts an arc twice the length of the radius of the circle.
E) One degree is the measure of a central angle that intercepts an arc half the length of the radius of the circle.
15. A biologist wants to know the width w of a river. From point A, the biologist walks
downstream 93 feet to point B and sights to point C (see figure). From this sighting, it is
determined that θ = 46°. How wide is the river? Round your answer to two decimals.
 
 1
2
16. Identify the components of the graph of the function and graph two periods. y  3sin 
A = __________
B = __________
D = __________
17. Identify the components of the graph of the function and graph two periods. y  2cos(4 x)  1
A = __________
B = __________
D = __________