Graph y=4sin(pix)

Problem

y=4*sin(π*x)

Solution

1. Identify the amplitude by looking at the coefficient of the sine function. The amplitude A is the absolute value of the coefficient 4

A=|4|=4

2. Determine the period using the formula P=(2*π)/B where B is the coefficient of x Here, B=π

P=(2*π)/π=2

3. Find the key points for one cycle by dividing the period into four equal intervals. Since the period is 2 the increments are 0.5

x=0,0.5,1,1.5,2

4. Calculate the y-coordinates for these key points using the function y=4*sin(π*x)

sin(π⋅0)=0⇒y=0

sin(π⋅0.5)=1⇒y=4

sin(π⋅1)=0⇒y=0

sin(π⋅1.5)=−1⇒y=−4

sin(π⋅2)=0⇒y=0

5. Plot the points (0,0) (0.5,4) (1,0) (1.5,−4) and (2,0) and connect them with a smooth sine wave.

Final Answer

y=4*sin(π*x)* has amplitude *4* and period *2

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