Graph y=4sin(x)
Problem
Solution
Identify the parent function and its properties. The base function is
y=sin(x) which has a period of2*π an amplitude of1 and passes through the origin(0,0) Determine the amplitude of the given function. The coefficient
4 in front of the sine function indicates a vertical stretch. The amplitude is|4|=4 Identify the period of the function. Since the coefficient of
x is1 the period remains2*π Find key points for one full cycle. Divide the period into four equal intervals to find the
x coordinates:0 π/2 π (3*π)/2 and2*π Calculate the y-coordinates for these key points:
At
x=0 y=4*sin(0)=0 At
x=π/2 y=4*sin(π/2)=4*(1)=4 At
x=π y=4*sin(π)=0 At
x=(3*π)/2 y=4*sin((3*π)/2)=4*(−1)=−4 At
x=2*π y=4*sin(2*π)=0
Sketch the graph by plotting the points
(0,0) (π/2,4) (π,0) ((3*π)/2,−4) and(2*π,0) and connecting them with a smooth wave.
Final Answer
The graph is a sine wave with an amplitude of
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