Question 510353: I am trying to graph y=2cos3(x-(pi/4)), how would I find the x and y-intercepts for this?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I am trying to graph y=2cos3(x-(pi/4)), how would I find the x and y-intercepts for this?
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Standard form of equation for cosine function: y=Acos(Bx-C), A=amplitude, Period=2π/B,
Phase-shift=C/B
For given equation, B, is factored out but equation could also be written: y=2cos(3x-3π/4).
This gives the function:
amplitude=2
B=3
Period=2π/B=2π/3=2.0944
1/4 period=2π/12=π/6=.5236
Phase-shift=C/B=(3π/4)/3=3π/12=π/4=.7854
note: graph on x-y coordinate system for one period, x-values in radians.
For the basic cosine curve of period 2π, the x intercepts are at π/2 and 3π/2, 1/4 and 3/4 period respectively.
For given cosine function, the curve starts at x=.7854, because of the shift. 1/4 period or .5236 later is the first x-intercept at x=.7854+.5236=1.3090. Similarly,3/4 period or 1.5078 later the second x-intercept is at x=.7854+1.5078=2.3562
..
For the y-intercept:
set=0, then solve for y
y=2cos(-3π/4)=2(-.7071)=-1.4142
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