How many cycles occur in the graph

Reference no: EM131510564

Assignemnt

Simplify the trigonometric expression. Show your work.

1. [1 / (1 + sin θ)] + [1 / (1 - sin θ)]

2. In ΔABC, ∠C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. Show your work.

a = 3, c = 19

3. Please show your work to find the mean and standard deviation of the data. Round to the nearest tenth.

20, 16, 18, 14, 9, 20, 16

4. What are the points of discontinuity? Are they all removable? Please show your work.

y= (x-5) / (x² - 6x + 5)

5. A sound wave is modeled with the equation y = ¼cos (2π/3) θ.

a. Find the period. Explain your method.

b. Find the amplitude. Explain your method.

c. What is the equation of the midline? What does it represent?

6. Paula spots a glider located at an angle of elevation of 42°. The distance between the glider and Paula is 3280 feet. To the nearest foot, what is the height of the glider h from the ground? Show your work.

7. What is the product in simplest form? State any restrictions on the variable. Please show your work.

[y² / (y - 3)] · [(y² - y 6) / (y² +y)]

Verify the identity. Justify each step.

8. (Tan θ + cot θ) = [1 / sin θ cos θ)]

9. Is there any bias in the survey question? Explain.

What do think would help students pay more attention in class?

10. Find the values of the 30th and 90th percentiles of the data. Please show your work.

129, 113, 200, 100, 105, 132, 100, 176, 146, 152

11. What is the quotient in simplified form? State any restrictions on the variable. Show Work.

[(a + 2) / (a - 5)] / [(a + 1) / (a² - 8a +15)]

12. Vance is designing a garden in the shape of an isosceles triangle. The base of the garden is 36 feet long. The function y = 18 tan θ models the height of the triangular garden.

2119_Isosceles Triangle.jpg

a. What is the height of the triangle when θ = 45^o?

b. What is the height of the triangle when θ = 55^o?

c. Vance is considering using either θ = 45^o or θ = 55^o for his garden. Compare the areas of the two possible gardens. Explain how you found the areas.

13. Verify the identity. Justify each step.

[sec θ / (csc θ - cot θ)] - [sec θ / (csc θ+ cot θ)] = 2csc θ

14. Compare the graphs of the inverse variations. Please provide at least 3 comparisons

y = (-0.2 / x) and y = (-0.3 / x)

15. Use a graphing calculator to solve the equation -3 cos t = 1 in the interval from 0 ≤ θ ≤ 2π. Round to the nearest hundredth.

16. The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.

h = 7 cos (πt / 3)

Solve the equation for t.

b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.

c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.

17. Consider the graph of the cosine function shown below.

a. Find the period and amplitude of the cosine function.

b. At what values of θ for 0 ≤ θ ≤ 2π do the maximum value(s), minimum values(s), and zeros occur?

18. Use the graph of the sine function y = 2 sin θ shown below.

2480_Sine Function Graph.jpg

a. How many cycles occur in the graph?
b. Find the period of the graph.
c. Find the amplitude of the graph.

19. Verify the Pythagorean Identity.

1 + cot² θ = csc² θ

20. Howard is flying a kite and wants to find its angle of elevation. The string on the kite is 32 meters long and the kite is level with the top of a building that he knows is 28 meters high.

To the nearest tenth of a degree, find the angle of elevation. Show your work.

Reference no: EM131510564

Questions Cloud

Write a problem to solve that can be translated to a system : Write a problem for a classmate to solve that can be translated to a system of two or more equations in at least two variables. Explain your answer.

What is the research problem that is being investigated : What is the research problem that is being investigated? What is the purpose of the research being conducted?

Create an online id that you can use in the real world : Let's get branded. A strong identity is important in a media dense society. Your goal is to create an online ID that you can use in the real world tomorrow

Explain the mission of the dash physician assistant program : The mission of the Dash Physician Assistant (PA) Program is to prepare PAs to provide compassionate, high-quality, patient-centered care as members.

How many cycles occur in the graph : How many cycles occur in the graph? Find the period of the graph. Find the amplitude of the graph. Find the period and amplitude of the cosine function.

How is burberry perceived in the market place : I need a paper that should be 2000 words long and use the quantitative and qualitative data from the case study.

Do you think cloning will become a good business opportunity : The healthcare community also is concerned about the business aspects of cloning.

Write a paper on vulnerable web applications : The paper should be doubled spaced, should be approximately 6 pages long, there should be no plagiarism, all sources used for this paper should be cited.

Generates prime number in c language : Give step-by-step analysis of an algorithm that generates prime number in C language.

User Account

All Pages