Graph -2sin(2pix)

Problem

y=−2*sin(2*π*x)

Solution

1. Identify the general form of the sine function y=A*sin(B*x+C)+D where A=−2 B=2*π C=0 and D=0

2. Determine the amplitude by taking the absolute value of A which is |−2|=2 The negative sign indicates a reflection across the x-axis.

3. Calculate the period using the formula P=(2*π)/|B|

P=(2*π)/(2*π)=1

4. Find the interval for one full cycle by dividing the period into four equal parts. The key x-values are 0 0.25 0.5 0.75 and 1

5. Evaluate the function at these key points to find the y-coordinates.

x=0⇒y=−2*sin(0)=0

x=0.25⇒y=−2*sin(π/2)=−2

x=0.5⇒y=−2*sin(π)=0

x=0.75⇒y=−2*sin((3*π)/2)=2

x=1⇒y=−2*sin(2*π)=0

6. Plot the points (0,0) (0.25,−2) (0.5,0) (0.75,2) and (1,0) and connect them with a smooth sine wave reflected over the x-axis.

Final Answer

y=−2*sin(2*π*x)

The graph is a sine wave with amplitude 2 period 1 and a reflection across the x-axis, passing through (0,0) (0.25,−2) (0.5,0) (0.75,2) and (1,0)

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