Graph y=1.5sin(x)

Problem

y=1.5*sin(x)

Solution

1. Identify the amplitude of the function. The amplitude is the absolute value of the coefficient of the sine function.

A=|1.5|=1.5

2. Determine the period of the function. For a function in the form y=A*sin(B*x) the period is calculated as (2*π)/B Here, B=1

Period=(2*π)/1=2*π

3. Find the key points for one full cycle by dividing the period into four equal intervals. The intervals occur at x=0 x=π/2 x=π x=(3*π)/2 and x=2*π

sin(0)=0⇒y=1.5*(0)=0

sin(π/2)=1⇒y=1.5*(1)=1.5

sin(π)=0⇒y=1.5*(0)=0

sin((3*π)/2)=−1⇒y=1.5*(−1)=−1.5

sin(2*π)=0⇒y=1.5*(0)=0

4. Plot the points and draw a smooth wave. The graph starts at the origin (0,0) reaches a maximum at (π/2,1.5) crosses the x-axis at (π,0) reaches a minimum at ((3*π)/2,−1.5) and returns to the x-axis at (2*π,0)

Final Answer

To graph y=1.5*sin(x) plot a sine wave with an amplitude of 1.5 and a period of 2*π

y=1.5*sin(x)

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