Graph y=cos(1/3x)

Problem

y=cos(1/3*x)

Solution

1. Identify the parent function and its properties. The function is of the form y=A*cos(B*x) where the parent function is y=cos(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=1/3

P=(2*π)/(1/3)

P=6*π

4. Find the key points by dividing the period into four equal intervals. The increment is (6*π)/4=(3*π)/2

5. Evaluate the function at these intervals starting from x=0

• At x=0 y=cos(0)=1

• At x=(3*π)/2 y=cos(π/2)=0

• At x=3*π y=cos(π)=−1

• At x=(9*π)/2 y=cos((3*π)/2)=0

• At x=6*π y=cos(2*π)=1

6. Plot the points (0,1) ((3*π)/2,0) (3*π,−1) ((9*π)/2,0) and (6*π,1) and connect them with a smooth wave.

Final Answer

y=cos(1/3*x)* has amplitude *1* and period *6*π

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