number of cycles per what ?
your curve is a horizontal shift of π/4 to the left of the curve
y = 2 cos (Ø/2) + 1
Given: y = 2 cos 1/2 (theta + pi/4) + 1
What is the number of cycles?
what is the horizontal shift?
3 answers
I'm not sure about the number of cycles, I think I'll assume it means the number of curves since there are 4 of them if i graph. Here is what I've already answered:
a. amplitude = 2
b. number of cycles = 4?
c. (is the phase shift also horizontal shift?) Phase shift = -(pi/4)
d. vertical shift = 1
a. amplitude = 2
b. number of cycles = 4?
c. (is the phase shift also horizontal shift?) Phase shift = -(pi/4)
d. vertical shift = 1
For the normal domain of 9 ≤ Ø ≤ 2π
period = 2π/(1/2) = 4π
so number of periods in the domain = 2π/4π = 1/2
look at Wofram's graph to confirm this
http://www.wolframalpha.com/input/?i=plot+y+%3D+2+cos+(1%2F2+(x+%2B+%CF%80%2F4))+%2B+1
Notice from a max to a min, which would be 1/2 of a period shows up as appr 6 (2π = appr 6.28)
period = 2π/(1/2) = 4π
so number of periods in the domain = 2π/4π = 1/2
look at Wofram's graph to confirm this
http://www.wolframalpha.com/input/?i=plot+y+%3D+2+cos+(1%2F2+(x+%2B+%CF%80%2F4))+%2B+1
Notice from a max to a min, which would be 1/2 of a period shows up as appr 6 (2π = appr 6.28)
2 answers