Graph y=-1/3*cos(1/3x)

Problem

y=−1/3*cos(1/3*x)

Solution

1. Identify the amplitude. The amplitude A is the absolute value of the coefficient of the cosine function.

|a|=|−1/3|=1/3

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

P=(2*π)/(1/3)=6*π

3. Find the phase shift and vertical shift. Since there are no constants added inside or outside the cosine function, both shifts are zero.

Phase Shift=0

Vertical Shift=0

4. Calculate the key points. Divide the period into four equal intervals of (6*π)/4=(3*π)/2 to find the xcoordinates for the intercepts, maximums, and minimums.

x=0,(3*π)/2,3*π,(9*π)/2,6*π

5. Evaluate the function at key points. Because of the negative sign, the graph starts at a minimum.

y(0)=−1/3

y*((3*π)/2)=0

y*(3*π)=1/3

y*((9*π)/2)=0

y*(6*π)=−1/3

6. Sketch the graph. Plot the points (0,−1/3) (3*π/2,0) (3*π,1/3) (9*π/2,0) and (6*π,−1/3) and connect them with a smooth wave.

Final Answer

y=−1/3*cos(1/3*x)

The graph is a cosine wave with amplitude 1/3 period 6*π and no vertical or horizontal shifts, reflected across the xaxis.

Want more problems? Check here!