Graph y=sin(7x)

Problem

y=sin(7*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| Given B=7 the period is (2*π)/7 This is the horizontal distance required for the function to complete one full cycle.

4. Find the key points by dividing the period into four equal intervals. The interval width is (2*π)/7÷4=π/14 The xcoordinates for one cycle starting at the origin are 0 π/14 π/7 (3*π)/14 and (2*π)/7

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

(0,0)

(π/14,1)

(π/7,0)

((3*π)/14,−1)

((2*π)/7,0)

6. Sketch the curve by plotting these points and connecting them with a smooth wave, then extending the pattern in both directions.

Final Answer

y=sin(7*x)

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