Graph 0.5cot(x)

Problem

0.5*cot(x)

Solution

1. Identify the parent function and its properties. The parent function is ƒ(x)=cot(x) which has a period of π and vertical asymptotes at x=n*π for any integer n

2. Determine the vertical stretch or compression. The coefficient 0.5 indicates a vertical compression by a factor of 0.5 This means the yvalues of the parent function are halved.

3. Locate the x-intercepts. The x-intercepts occur where cot(x)=0 which is at x=π/2+n*π These points remain unchanged by the vertical compression.

4. Identify key points for one period. In the interval (0,π) the parent function passes through (π/4,1) and ((3*π)/4,−1) For 0.5*cot(x) these points become (π/4,0.5) and ((3*π)/4,−0.5)

5. Sketch the graph. Draw vertical asymptotes at x=0,π,2*π,… and plot the key points to draw the decreasing curves in each period.

Final Answer

y=0.5*cot(x)

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