Chapter 5.2, Problem 28E

7. The number of visible sun spots varies rhythmically from 10 to 110 per year over a period of eleven years. The 110 max last occurred in the year 2014. a.) b.) Write a sinusoidal function N (t) to model that number of sun spots per year, where t is in years past the year 2014. What number of sun spots does your function predict for the year 2018?

18. Fill in each blank with an interval of real numbers. (a) The function f(x) = cosx has domain and range (b) The function f(x) = csc x has domain and range (c) The restricted tangent function has domain and range (d) The function f(x) = sec-1x has domain and range

3 Consider the function g(x)= sin -- 1 with restricted domain 0,4|. Find and identify any relative and absolute extrema. Write each extrema as an ordered pair.

Sketch a graph of the function f(x) = 2 – 2 cos(x). Click the appropriate button based on which points you want to graph. Middle = Amplitude = Period = Shift = **The graph of y = cos x is given on the graph. 7+

Plot the graphs of f(x) = x(x - 3) (x + 3) and g(x) = cos 2 x together on the same set of axes and over the interval [-20, 20]. Use the PlotRange option to adjust the range of the viewing window so that their points of intersection are visible.

The following represents the graph of the function: OS(x) = cos x- cos x+- 2 2 X. TU2 3 T/ 2 (points) Based on the graph of this function do the following: a. Use your understanding of how to identify the parameters of the sinusoidal function y = asin(hx +c) + d or y = acos(hx +c)+d_to write the equation of a simpler function p(x) that describes the graph. Explain your choices. b. Check the answer you obtained in (a) by graphing the new function p(x). Obtain a printout of the graph. Explain how you used your graphing calculator to verify that your answer is сопеct. c. Verify algebraically that the two equations are equivalent.

The height of a wave can be represented by the function y = 3 cos (pi/8 * (x - 6)) + 4 with time in What are the maximum and heights, and when do on the interval 0 < z < 24

In the graph below, the red graph is y = cos x. What is the function represented by the blue graph? (-4x/3, 1) Select one: (-3,-1) O b. 0 a. y = = cos(x+3) y = cos(x - 2) O c. y = cos(x + 2) ○ d. y = cos(x) (2x/3, 1)

Graph the function f(x) = cos(x) + sin(x) by first graphing y = cos x and y = sin x on the same axes then pick a selection of x values and add their values together to get y values for f(x).  When you've got enough points to see the trend of the graph, connect them to get the final result.