Graph y=6sin(2x)

Problem

y=6*sin(2*x)

Solution

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

A=|6|=6

2. Determine the period using the coefficient of x which is B=2 The formula for the period P of a sine function is P=(2*π)/B

P=(2*π)/2=π

3. Calculate the phase shift and vertical shift. Since there are no constants added inside or outside the sine function, both shifts are zero.

Phase Shift=0

Vertical Shift=0

4. Find the key points for one cycle by dividing the period into four equal intervals. The interval width is π/4 The xcoordinates are 0 π/4 π/2 (3*π)/4 and π

x=0⇒y=6*sin(0)=0

x=π/4⇒y=6*sin(π/2)=6

x=π/2⇒y=6*sin(π)=0

x=(3*π)/4⇒y=6*sin((3*π)/2)=−6

x=π⇒y=6*sin(2*π)=0

5. Sketch the graph by plotting these points and drawing a smooth sine wave. The graph oscillates between y=6 and y=−6 with a full cycle completed every π units.

Final Answer

y=6*sin(2*x)

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