Graph y=4sin(2x)

Problem

y=4*sin(2*x)

Solution

1. Identify the amplitude by looking at the coefficient of the sine function. The amplitude A is |4| which means the graph oscillates between y=4 and y=−4

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

P=(2*π)/2

P=π

3. Calculate the interval for the key points by dividing the period by 4

Interval=π/4

4. Find the key points for one cycle starting at x=0 The xcoordinates are 0 π/4 π/2 (3*π)/4 and π

5. Evaluate the function at these xcoordinates to find the yvalues.

(0,0)

(π/4,4)

(π/2,0)

((3*π)/4,−4)

(π,0)

6. Sketch the curve by plotting these points and connecting them with a smooth sine wave that repeats every π units.

Final Answer

y=4*sin(2*x)

The graph is a sine wave with amplitude 4 period π and no phase shift.

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