Posted by **tamara** on Friday, July 2, 2010 at 4:12pm.

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?

- trig -
**Damon**, Friday, July 2, 2010 at 5:20pm
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

- trig -
**Reiny**, Friday, July 2, 2010 at 5:34pm
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.

- trig -
**Damon**, Friday, July 2, 2010 at 6:10pm
humm, looks like we agree in the end :)

- Damon - trig -
**Reiny**, Friday, July 2, 2010 at 6:31pm
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.

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