Graph y=3sin(4x)

Problem

y=3*sin(4*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 3

|A|=3

2. Determine the period of the function using the formula P=(2*π)/b where b is the coefficient of x Here, b=4

P=(2*π)/4

P=π/2

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 by dividing the period into four equal intervals. The interval width is (π/2)/4=π/8 The xcoordinates are 0 π/8 π/4 (3*π)/8 and π/2

Interval=π/8

5. Evaluate the function at these key points to find the ycoordinates.

(0,0)

(π/8,3)

(π/4,0)

((3*π)/8,−3)

(π/2,0)

6. Sketch the graph by plotting these points and connecting them with a smooth sine wave starting from the origin, reaching a maximum at y=3 and a minimum at y=−3

Final Answer

y=3*sin(4*x)

The graph is a sine wave with amplitude 3 period π/2 and no phase shift.

Want more problems? Check here!