By what fraction of the period of f(x)=10 cos(7 x) has the graph of f(x) been shifted to obtain the graph of g(x)=10 cos(7x- pi/2). how do I approach this and solve for the fraction shift and the domain and range?

Answer 1

2 pi is a whole circle or period
pi/2 is a quarter of a circle or period

the domain of this function is all real x, in other words x can be any real number positive or negative
However cosine is between -1 and +1 so range is between -10 and +10

Answer 2

the period of y = 10cos(7x) is 2π/7

rewriting the second as
y = 10cos 7(x - π/14) we can see that the phase shift was
π/14 to the right.

so what fraction is that phase shift of the period?
(π/14)/(2π/7)
or
1/4 of the phase shift.

Answer 3

humm, looks like we agree in the end :)

Answer 4

Damon, when I opened the page and started to answer this question, I left it alone to watch the end of the WorldCup football game, and when I resumed I did not refresh the page, thus did not see your answer was already posted.