Question 447237: how do you find the amplitude of y=-2cos1/3x
how do you find the period, the phase shift and the tick marks for y=-4cos(x-3.14/3)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! how do you find the amplitude of y=-2cos1/3x
how do you find the period, the phase shift and the tick marks for y=-4cos(x-3.14/3)
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Standard form for the cosine function: y=A cos(Bx-C), with |A| being the amplitude, period=2π/B and C/A=phase-shift.
For given first cosine function: y=-2cos (x/3)
Amplitude=2
B=1/3
period=2π/B=6π
phase shift=0
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For given second cosine function: y=-4cos(x-π/3)
Amplitude=4
B=1
period=2π/1=2π
phase shift=π/3=4π/12 (to the right)
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calculating tick marks:
y-intercept
set x=0
y=-4cos(-π/3)=-4*1/2=-2
1/4 period=2π/4=6π/12
first tick mark at x=π/3 or 4π/12
after this tick add 1/4 period or 6π/12 four more times after this to end up with the following tick marks:
4π/12, 10π/12, 16π/12, 22π/12 and 28π/12
You will now have the following points to plot the given cosine function:
(0,-2)(y-intercept), (4π/12,0), (10π/12,4),(16π/12,0), (22π/12,-4) and (28π/12,0)
Note that I have left all the fractions in twelfths for ease of adding the fractions. In the final answer you should reduce all the fractions to lowest terms. Also, note that the difference between the first tick and the last tick is 28π/12-4π/12=24π/12=2π as it should be for one period. Sorry, I don't have the means to plot it for you.
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