Graph y=sin(4x)

Problem

y=sin(4*x)

Solution

1. Identify the parent function and its properties. The function is of the form y=A*sin(B*x) where the parent function is y=sin(x)

2. Determine the amplitude, which is the absolute value of the coefficient A Here, A=1 so the amplitude is 1 This means the graph oscillates between y=1 and y=−1

3. Calculate the period using the formula P=(2*π)/B In this function, B=4

P=(2*π)/4

P=π/2

4. Find the key points by dividing the period into four equal intervals. The interval width is (π/2)/4=π/8 The xcoordinates for one cycle starting at x=0 are 0 π/8 π/4 (3*π)/8 and π/2

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

sin(4⋅0)=0

sin(4⋅π/8)=1

sin(4⋅π/4)=0

sin(4⋅(3*π)/8)=−1

sin(4⋅π/2)=0

6. Plot the points (0,0) (π/8,1) (π/4,0) ((3*π)/8,−1) and (π/2,0) and connect them with a smooth sine wave.

Final Answer

y=sin(4*x)* has amplitude *1* and period π/2

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