Assignment Submission For this assignment you submit answers

Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. Use a graphing utility to approximate the solutions of the equation in the interval [0, 2 pi). 7 cos(x - 21 pi/2) -7 sin^2 x= 0 x = The equation of a standing wave is obtained by adding the displacements of two waves traveling in opposite directions (see figure). Assume that each of the waves has amplitude A, period T, and wavelength A. If the models for these waves are Y_1 = A cos 2 pi (t/T - x/lambda) and y_2 = A cos 2 pi (t/T + x/lambda) show that y_1 + y_2 = 2A cos 2pit/T cos 2 pi x/lambda

Solution

Writing the first equation:

7cos(x-21/2*pi)-7(sinx)^2=0

=>cos(x-21/2*pi)-(sinx)^2=0

=>cos(x)cos(21*pi/2)+sin(x)*sin(21*pi/2)=(sin(x))^2

=>0+sin(x)*sin(21*pi/2)=(sin(x))^2

=>sin(x)=(sin(x))^2

Solution to the above equation is:

sin(x)=0, sin(x)=1

sin(x)=0, x=0,pi

sin(x)=1, x=3*pi/2

x=[0,3*pi/2,pi]