Graph y=cos(3x)

Problem

y=cos(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=3

P=(2*π)/3

4. Find the key points by dividing the period into four equal increments. The increment size is P/4=(2*π)/12=π/6 The xcoordinates for one cycle starting at x=0 are 0 π/6 π/3 π/2 and (2*π)/3

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

cos(3⋅0)=1

cos(3⋅π/6)=0

cos(3⋅π/3)=−1

cos(3⋅π/2)=0

cos(3⋅(2*π)/3)=1

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

Final Answer

y=cos(3*x)

The graph is a cosine wave with amplitude 1 and period (2*π)/3

Want more problems? Check here!