3. The average temperature in Detroit, Michigan on any given day of the year can be modeled by T(t) = 27 sin(0.0172(t- 115) + 50, where T is the temperature in degrees Fahrenheit and t is the number of days elapsed since January 1st. (a) State the period (in days), the amplitude, the vertical shift, and the phase shift. Interpret all four of these in the context of the real-world situation being modeled.

3. The average temperature in Detroit, Michigan on any given day of the year can be modeled by T(t) = 27 sin(0.0172(t- 115) + 50, where T is the temperature in degrees Fahrenheit and t is the number of days elapsed since January 1st. (a) State the period (in days), the amplitude, the vertical shift, and the phase shift. Interpret all four of these in the context of the real-world situation being modeled.

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

See similar textbooks

Similar questions

4. Find the period and phase shift of each of the following functions: a) y = -cot(6x - 4) b) y = 2 sec(x + n)
Compare the phase shift and amplitude of y=-cos(x-180∘) and y=-2sin(x-90∘). Which of the following choices is the correct comparison? a The cosine function has a phase shift that is 12 that of the sine function and in the same direction; the amplitude of the cosine function is 2 times that of the sine function. b The cosine function has a phase shift that is 12 that of the sine function and in the opposite direction; the amplitude of the cosine function is 12 that of the sine function. c The cosine function has a phase shift that is 2 times larger than the phase shift of the sine function and in the same direction; the amplitude of the cosine function is 12 that of the sine function. d The cosine function has a phase shift that is 2 times larger than that of the sine function and in the opposite direction; the amplitude of the cosine function is 2 times that of the sine function.
write an equation of the form y=a sin [k(x-b)] with the given amplitude : pi period:4, and phase shift:- 1/3.
Consider the following function. y = -3.5 cosx + 4) (a) Using pencil and paper, not a graphing utility, determine the amplitude, period, and phase shift for the function. amplitude period phase shift (b) Use a graphing utility to graph the function for two complete cycles. [In choosing an appropriate viewing rectangle, you will need to use the information obtained in part (a).] y y 4 4| 2. -12 \12 я - 12 12 л - 6 -2 2 -4 y y 4 4- 2 2 -3 12 л - 3 12 л - 9 -2 (c) Use the graphing utility to estimate the coordinates of the highest points on the graph. (Round your answers to two decimal places.) (x, y) = (smaller x-value) (x, y) = (| (larger x-value) Use the graphing utility to estimate the coordinates of the lowest points on the graph. (Round your answers to two decimal
The San Francisco Bay tides vary between 1 foot and 7 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? A. Amplitude = 6 feet; period = 8 hours; midline: y = 4 B. Amplitude = 6 feet; period = 4 hours; midline: y = 3 C. Amplitude = 3 feet; period = 8 hours; midline: y = 4 D. Amplitude = 3 feet; period = 4 hours; midline: y = 3
Suppose y = 37 Cos (-4t + 5) + 9. In your answers, enter 'pi' for T. (a) The amplitude of the graph is (b) The period of the graph is (c) The phase (horizontal shift) of the graph is (d) The midline (vertical shift) of the graph is y
Write the equation for a cosine function with amplitude π,period 1, and phase shift -2.
The graph of a sine function has an amplitude of 4, a midline of y = 2, and a period of 10. There is no phase shift. The graph is reflected over the x-axis. What is the equation of the function?
1. One cycle of a sine function begins at x = 3 and ends at x = a. Determine the period of the function. b. Determine the phase shift of the function. c. Write the equation of the function in the form y = sin k(x - d)