Math
Aanand
Test2.pdf
MATH 1713 Test 2 Week 8
Names: Name: Date:
Read the following instructions carefully before beginning this part of the test.
Instructions:
• This assignment is to be completed on your own.
• You have until F 03/05/21 at 11:59 PM to complete the following problems.
• Complete on separate paper, OR print & work in the space provided, and scan as a single PDF (use OneDrive or Adobe Scan app, e.g.), then upload to corresponding Blackboard assignment (Tests) for submission. Make sure you get a confirmation for your submission. You may also digitally annotate the provided PDF.
• These assignment pages do not need to be included with your submission.
• You are expected to clearly label each problem and answer.
• To receive full credit you must show all work and simplify each answer as much as possible. Correct notation must be used and any explanations must be clear.
• All answers should be exact, no decimals unless specified.
• Cheating will not be tolerated. This includes, but is not limited to, the following:
– No talking with others about the test
– No sharing answers or copying the work of others
– The only aids you may have are resources/content provided by the instructor
The use of any other resources will be considered a violation of the ECU Academic Integrity Policy and you will automatically receive a 0 on the assessment. Such violations will also be reported to the University.
• Test 2 is worth a total of 75 points: Make sure you answer each question completely.
By submitting this assignment, you agree that you have read, understand, and will follow all of the above instructions.
Remember to show all work and use correct notation to earn full credit. All answers should be exact - no decimals, unless specified.
1. (5 points) Fill in all ten blanks in the first two quadrants of the unit circle.
(1, )
(√ 3 2 , 1 2
) (
, √ 2 2
) (
, √ 3 2
)(0, )( , √ 3 2
) ( − √ 2 2 , √ 2 2
) (
, 1 2
)
( , 0) 0
π 4
π 3
π 2
3π 4
5π 6
2. (2 points) Convert from degrees into radians: 36◦
Leave your answer as a multiple of π. You must show work to earn credit.
3. (2 points) Convert from radians into degrees: − 2π
3 You must show work to earn credit.
4. (5 points) For what values of θ is cos θ = 0. Your answer should include all possible solutions and should be in terms of radians.
REMEMBER TO SHOW ALL WORK!!!
5. (6 points) Calculate the following trig function value using a reference angle. You must show your work, just an answer will not receive full credit. Your response must include the following:
(a) Sketch of the angle in standard position.
(b) What Quadrant is the angle in?
(c) What reference angle did you use?
sin
( 5π
3
)
6. (6 points) Find all angles θ (there should be two) in [0, 2π] such that cos θ = 1 2 .
Your response must include the following:
(a) What Quadrants are these angles in?
(b) What reference angle did you use?
Page 2
REMEMBER TO SHOW ALL WORK!!!
7. (5 points) Find the exact area of the sector of a circle of radius 10 cm intercepted by a central angle of 120◦. Your answer should be exact (no decimals) and include units.
8. (8 points) A Ferris wheel has radius 50 feet. A person takes a seat and then the wheel turns 120◦ in 30 seconds.
(a) What is the angular speed of the person riding the wheel? Your answer should be exact (no decimals) and include units.
(b) What is the linear speed of the person riding the wheel? Your answer should be exact (no decimals) and include units.
Page 3
REMEMBER TO SHOW ALL WORK!!!
9. (6 points) Consider the function graphed below:
x
y
π 2
π 3π 2
2π−π 2
−π−3π 2
−2π
1
-1
2
-2
(a) What is the amplitude of the function?
(b) What is the period of the function?
(c) What is the phase shift/horizontal translation?
(d) What is the vertical shift?
(e) What is the function?
10. (6 points) Consider the trig function below:
y = −3 sin (
1
3
( x −
π
2
)) + 6
(a) What is the amplitude of the function?
(b) What is the period of the function?
(c) What is the phase shift/horizontal translation?
(d) What is the vertical shift?
(e) What does the negative at the beginning do?
Page 4
REMEMBER TO SHOW ALL WORK!!!
11. (2 points) Which one of these six trigonometric functions has a period of π and passes through the point (0, 0)?
A. y = sin(x)
B. y = cos(x)
C. y = tan(x)
D. y = csc(x)
E. y = sec(x)
F. y = cot(x)
12. (2 points) Which one of these six trigonometric functions has a period of 2π and a
vertical asymptote of x = π
2 ?
A. y = sin(x)
B. y = cos(x)
C. y = tan(x)
D. y = csc(x)
E. y = sec(x)
F. y = cot(x)
13. (2 points) Which of the following is the equation of the cosine function with period 4π and a vertical translation of 3 units up?
A. y = 3 cos(2x)
B. y = cos(x + 2)
C. y = cos(4πx) + 3
D. y = cos(x 2 ) + 3
Page 5
REMEMBER TO SHOW ALL WORK!!!
14. (7 points) Consider the function y = sin(x) − 1. (a) Complete the following table:
x −2π −3π/2 −π −π/2 0 π/2 π 3π/2 2π
y
(b) Now graph (by hand - do not use a graphing calculator or Desmos, e.g.) two periods of the function y = sin(x) − 1.
x
y
π 2
π 3π 2
2π−π 2
−π−3π 2
−2π
1
-1
2
-2
(c) What transformation to the graph of y = sin(x) corresponds to your graph above?
Page 6
REMEMBER TO SHOW ALL WORK!!!
15. (6 points) One period of a trig function is graphed below. Note the points (π/4, 2) and (−π/4,−2) are on the graph. Determine the specific function graphed. Note this includes determining values of a, b, c, and d, as necessary.
x
y
π 2
ππ 4
−π 4
3π 4
−3π 4 −π
2 −π
1
-1
2
-2
3
-3
(a) a=?
(b) b =?
(c) c =?
(d) d =?
(e) Function:
Page 7
REMEMBER TO SHOW ALL WORK!!!
16. (5 points) Below is graphed the function y = sin x. Graph (by hand - do not use a graphing calculator or Desmos, e.g.) the function y = csc x on the same graph. Include any vertical asymptotes as well.
x
y
π 2
π 3π 2
2π−π 2
−π−3π 2
−2π
1
-1
2
-2
3
-3
Page 8
