Graph y=5cot(x)

Problem

y=5*cot(x)

Solution

1. Identify the parent function and its properties. The function y=cot(x) has vertical asymptotes where sin(x)=0 which occur at x=n*π for any integer n

2. Determine the period of the function. The period of cot(x) is π and since there is no horizontal scaling factor, the period of y=5*cot(x) remains π

3. Identify the vertical stretch. The coefficient 5 indicates a vertical stretch by a factor of 5 This means the function will decrease more steeply than the standard cotangent graph.

4. Find key points within one period (0,π) At x=π/4 y=5*cot(π/4)=5*(1)=5 At x=π/2 y=5*cot(π/2)=5*(0)=0 At x=(3*π)/4 y=5*cot((3*π)/4)=5*(−1)=−5

5. Sketch the asymptotes at x=0 x=π and x=2*π Plot the key points and draw the decreasing curves between the asymptotes to complete the graph.

Final Answer

y=5*cot(x)

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