SOLUTION: Please help Rewrite r(t) = -4 sin (5t + pi/2) + 7 as, v(t), a function of cosine V(t)=_______

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Question 1115325: Please help
Rewrite r(t) = -4 sin (5t + pi/2) + 7 as, v(t), a function of cosine
V(t)=_______
Answer by greenestamps(13208) About Me  (Show Source):
You can put this solution on YOUR website!


A cosine function shifted one-quarter period to the right is the same as a sine function:



So the given function

r%28t%29+=+-4sin%285t%2Bpi%2F2%29%2B7

is the same as the function

v%28t%29+=+-4cos%28%285t%2Bpi%2F2%29-pi%2F2%29%2B7

or

v%28t%29+=+-4cos%285t%29%2B7

There are of course an infinite number of equivalent functions using either sine or cosine.

For example, a cosine function shifted a quarter period to the left is the same as a negative sine function:



So another cosine function equivalent to the given sine function is

v%28t%29+=+4cos%28%285t%2Bpi%2F2%29%2Bpi%2F2%29%2B7

or

v%28t%29+=+4cos%285t%2Bpi%29%2B7