Question 730356: How do I graph y=3tan(2x)? Can you please go step by step, I have a test coming up.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! graph y=3tan(2x)
Equation of tan function: y=Atan(Bx-C), period=π/B, phase shift=C/B, A is a multiplier that stretches the curve vertically.
For given equation: y=3tan(2x)
A=3
B=2
period=π/B=π/2
1/4 period=π/8
C=0
phase shift: none
..
coordinates of graph for one period: (0 to π/2) with A=1
(0,0), (π/8,1), (π/4, u.d.), (3π/8,-1), (π/2,0)
final configuration with A=3
(0,0), (π/8,3), (π/4, u.d.), (3π/8,-3), (π/2,0)
..
Notes:
tan=sin/cos
At beginning of period or 0, sin=0 and cos=1, so tan=0/cos=0
At 1/4 period or π/8, sin=1,cos=1, so tan=sin/cos=1
At 1/2 period or π/4, sin=1,cos=0, so tan=sin/0=undefined
At 3/4 period or 3π/8, sin=-1 and cos=1, so tan=sin/cos=-1
At end of period or π/2, sin=0 and cos=1, so tan=0/cos=0
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