SOLUTION: please help me graph the function: 4sin(2x+pi/3)-2

Question 602788: please help me graph the function: 4sin(2x+pi/3)-2
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
please help me graph the function:
4sin(2x+pi/3)-2
**
Equation for sin function: y=Asin(Bx-C), A=amplitude, period=2π/B, phase shift=C/B
For given sin function: 4sin(2x+pi/3)-2
A=4
B=2
C=π/3
period=2π/B=2π/2=π
(1/4) period=π/4
phase shift=C/B=(π/3)/2=π/6 (to the left)
Vertical shift= 2units down
..
Graphing given sin function for one period (π):
..
Coordinates for basic sin function: sin(2x)
(0,0), (π/4,1), (π/2,0), (3π/4,-1), (π,0)
..
phase shift curve π/6 left: sin(2x+π/3)
(-π/6,0), (π/12,1), (π/3,0), (π/4,-1), (5π/6,0)
..
Increase amplitude to 4: 4sin(2x+π/3)
(-π/6,0), (π/12,4), (π/3,0), (π/4,-4), (5π/6,0)
..
Vertical shift 2 units down: 4sin(2x+π/3)-2
(-π/6,0), (π/12,2), (π/3,0), (π/4,-6), (5π/6,0)
y-intercept:
set x=0
y=4sin(pi/3)-2
y=4*√3/2-2=2√3-2≈1.464
This is the final configuration for the graph of given sin function: 4sin(2x+pi/3)-2

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