Graph y=cos(4x)

Problem

y=cos(4*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. The coefficient A is 1 so the amplitude is |1|=1 This means the graph oscillates between y=1 and y=−1

3. Calculate the period. The period P of a cosine function is given by (2*π)/|B| Here, B=4

P=(2*π)/4

P=π/2

4. Find the critical points. Divide the period into four equal intervals to find the xcoordinates for the maximums, minimums, and intercepts. The interval width is (π/2)/4=π/8

(x_0)=0

(x_1)=π/8

(x_2)=(2*π)/8=π/4

(x_3)=(3*π)/8

(x_4)=(4*π)/8=π/2

5. Evaluate the function at these critical points to determine the ycoordinates.

cos(4⋅0)=1

cos(4⋅π/8)=0

cos(4⋅π/4)=−1

cos(4⋅(3*π)/8)=0

cos(4⋅π/2)=1

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

Final Answer

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

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