SOLUTION: I don't know where else to turn, I've asked my tutors my teacher and peers to explain how to graph sin,cos,sec,csc,tan,cot with phase shifts but nothing seems to work or I am just

Question 964315: I don't know where else to turn, I've asked my tutors my teacher and peers to explain how to graph sin,cos,sec,csc,tan,cot with phase shifts but nothing seems to work or I am just stupid...how do I set them up? my main confusing is all to do with the phase shifts, everything else makes sense to me. I know the amp, the periodicity. But it's when it comes to shifting everything right or left where the confusion sets in. The process of doing this is troublesome and I keep hitting brick walls. For instance, my teacher asked us to draw the graph of: y=10tan(3t-pi/8) I know I would rerrange like y=10tan3(t-pi/24) but after that I wouldn't know what to do, I just want to know what the points are going to be on the graph and how to derive them...I am at my witts end here. Please help me understand.
Thanks!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The best place to start is to first graph the basic function without any shifting.
For example, take the tan function your teacher gave you: y=10tan(3t-pi/8)
This equation takes the form: y=A*tan(Bx-C), A=multiplier, period=π/B, C/B=phase shift
For your given tan function: period=π/B=π/3
1/4 period=(π/3)/4=π/12≈0.26
coordinates for one period: (-π/6, u.d.), (-π/12, -1), (0, 0), (π/12, 1), (π/6, u.d.)
multiply y-coordinates by 10: (-π/6, u.d.), (-π/12, -10), (0, 0), (π/12, 10), (π/6, u.d.)
phase shift=C/B=(π/8)/3=π/24 (shift to right)
coordinates for final configuration: (-3π/24, u.d.), (-π/24, -10), (π/24, 0), (3π/24, 10), (5π/24, u.d.)
u.d.=undefined
..
Form of equation for sin: y= Asin(Bx-C), A=amplitude, Period=2π/B, Phase shift=C/B
Form of equation for cos: y= Acos(Bx-C), A=amplitude, Period=2π/B, Phase shift=C/B
note: this is just one of the ways I do it. There may be other ways. Hope this helps.
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