Math Grade 11 Sinusoidal functions

Sinusoidal functions. math grade 11.

#1) Determine the equation of each graph in the form y = acos(bx). 

#2) Determine the equation of each graph in the form of y = asin (bx). 

 

Both Graphs are not posted here, but i have a link for each graph below:

Graph 1. http://i515.photobucket.com/albums/t358/moeen11/latest.png

Graph 2. http://i515.photobucket.com/albums/t358/moeen11/lates1.png

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We are asked to only answer 1 question, but you should be able to answer the other using similar reasoning:

In graph 1 we see that there is a maximum at y=4, a minimum at y=-4, and the period is 1440. We are asked to write an equation for the sinusoid as a transformation of the cos graph and the sin graph.

(1) The graph is already in the shape of the cos, so we will begin there.

The general form is `y=Acos(B(x-h))+k` where A gives the amplitude (and if A<0 it reflects the graph across the horizontal axis), the period is found from B (`p=(360)/B` ), h is a horizontal translation (phase shift) and k is a vertical translation (its effect is to move the midline.)

Since the max is 4 and the min is -4, the midline is `y=(4+-4)/2==>y=0` so k=0. Also the amplitude is `A=(4-(-4))/2=4`

The graph is already in the proper position for the cos, so there is no phase shift. The period is ``1440, so `B=360/p=360/1440=1/4`

Thus the equation is `y=4cos(x/4)`

(2) In order to write the equation in terms of sin, we realize that the period and amplitude stay the same as well as the lack of vertical translation. There is only a phase shift to deal with.

The phase shift is 90 to the left, so the equation is `y=sin(x/4+90)`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial