Graph y=3cos(3x)

Problem

y=3*cos(3*x)

Solution

1. Identify the amplitude by looking at the coefficient in front of the cosine function.

A=|3|=3

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

P=(2*π)/3

3. Calculate the phase shift and vertical shift. Since there are no horizontal or vertical translations, both are zero.

Phase Shift=0

Vertical Shift=0

4. Find the key points for one cycle by dividing the period into four equal intervals of length P/4=π/6

(x_0)=0

(x_1)=π/6

(x_2)=π/3

(x_3)=π/2

(x_4)=(2*π)/3

5. Evaluate the function at these key xvalues to find the corresponding ycoordinates.

(0,3)

(π/6,0)

(π/3,−3)

(π/2,0)

((2*π)/3,3)

6. Sketch the graph by plotting these points and connecting them with a smooth, periodic wave.

Final Answer

y=3*cos(3*x)

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