Graph y=2cos(pi/2x)

Problem

y=2*cos(π/2*x)

Solution

1. Identify the amplitude by looking at the coefficient of the cosine function. The amplitude A is the absolute value of the coefficient 2

A=|2|=2

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

P=(2*π)/π/2=4

3. Find the key points by dividing the period into four equal intervals. Since the period is 4 the increments are 4/4=1 The xvalues for one cycle starting at x=0 are 0, 1, 2, 3, 4$.

4. Calculate the yvalues for each key xvalue by substituting them into the equation y=2*cos(π/2*x)

x=0⇒y=2*cos(0)=2

x=1⇒y=2*cos(π/2)=0

x=2⇒y=2*cos(π)=−2

x=3⇒y=2*cos((3*π)/2)=0

x=4⇒y=2*cos(2*π)=2

5. Plot the points (0,2) (1,0) (2,−2) (3,0) and (4,2) on a coordinate plane and connect them with a smooth wave.

Final Answer

y=2*cos(π/2*x)

The graph is a cosine wave with amplitude 2 period 4 and no phase shift. Key points for one cycle are (0,2),(1,0),(2,−2),(3,0),(4,2)

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