Graphing sin and cos functions

  • Thread starter jayare81
  • Start date
  • #1
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Homework Statement



plot x(t) = 10cos((pi*t)-(pi/4))

Homework Equations



pi/4 is the shift to the right

10 is the amplitude of the graph

pi is the radian frequency

The Attempt at a Solution



so i got the amplitude and shift to the right by pi/4 part but as for the radian frequency, my plot doesnt seem right. does pi mean that one cos wave occurs in a pi interval? thanks in advance

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,913
Yes. pi is the angular frequency, w. How is it related to the time period, T?

ehild
 
  • #3
35,125
6,871

Homework Statement



plot x(t) = 10cos((pi*t)-(pi/4))

Homework Equations



pi/4 is the shift to the right
I don't think so. You could write this function as x(t) = 10 cos(pi(t - 1/4)). The graph of x(t) = 10 cos(pi*t) has two transformations: a vertical expansion by a factor of 10 (that's your amplitude), and a compression toward the vertical axis by a factor of pi. This compression means that instead of having t intercepts at +/-pi/2, +/-3pi/2, +/-5pi/2, and so on, x(t) = 10 cos(pi*t) has t intercepts at +/-1/2, +/-3/2, +/-5/2, and so on.
The -1/4 term causes a shift to the right by 1/4 unit of the graph of x(t) = 10 cos(pi*t).
10 is the amplitude of the graph

pi is the radian frequency

The Attempt at a Solution



so i got the amplitude and shift to the right by pi/4 part but as for the radian frequency, my plot doesnt seem right. does pi mean that one cos wave occurs in a pi interval? thanks in advance

Homework Statement





Homework Equations





The Attempt at a Solution

 
  • #4
2
0
thanks for the help! T is 2pi/w so the period i got was 2. one cos wave occurs within 0-2
 
  • #5
ehild
Homework Helper
15,543
1,913
Yes, but do not forget that it is shifted, so its has the maximum value where (pi*t)-(pi/4)=0.

ehild
 

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