Graph y=3cos(4x)

Problem

y=3*cos(4*x)

Solution

1. Identify the amplitude by looking at the coefficient of the cosine function. The amplitude is |3| which means the graph oscillates between y=3 and y=−3

2. Determine the period using the formula P=(2*π)/b where b=4

P=(2*π)/4

P=π/2

3. Find the key points by dividing the period into four equal intervals. The distance between each key point is P/4=π/8 The xcoordinates for one cycle starting at x=0 are 0,π/8,π/4,(3*π)/8, and π/2

4. Calculate the y-coordinates for the key points. Since there is no vertical shift or phase shift, the points follow the pattern (max, zero, min, zero, max) for a positive cosine function.

(0,3),(π/8,0),(π/4,−3),((3*π)/8,0),(π/2,3)

5. Sketch the curve by plotting these points and connecting them with a smooth, wave-like shape, then extending the pattern in both directions.

Final Answer

y=3*cos(4*x)* has amplitude *3* and period π/2

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