Unit 2 Part 2 Tangent and Cotangent Graphing

Front

What is the cotangent function?

Back

The cotangent function, denoted as cot(x), is the reciprocal of the tangent function. It is defined as cot(x) = cos(x)/sin(x).

Front

What is the midline of a cotangent graph?

Back

The midline of a cotangent graph is the horizontal line that represents the average value of the function. For the function y = a cot(bx + c) + d, the midline is y = d.

Front

How do you determine the phase shift of a cotangent graph?

Back

The phase shift of a cotangent graph is determined by the value of c in the function y = a cot(bx + c) + d. The phase shift is calculated as -c/b.

Front

What is the period of the cotangent function?

Back

The period of the cotangent function is π. For the function y = a cot(bx + c) + d, the period is π/|b|.

Front

Where do the asymptotes of the cotangent graph occur?

Back

The asymptotes of the cotangent graph occur where the sine function is equal to zero, which is at x = nπ, where n is an integer.

Front

What is the relationship between the cotangent and tangent functions?

Back

The cotangent function is the reciprocal of the tangent function: cot(x) = 1/tan(x).

Front

How does the amplitude affect the cotangent graph?

Back

The cotangent function does not have an amplitude like sine or cosine functions because it approaches infinity and negative infinity.

Front

What is the effect of the parameter 'a' in the cotangent function?

Back

The parameter 'a' in the cotangent function y = a cot(bx + c) + d affects the vertical stretch or compression of the graph.

Front

What is the effect of the parameter 'd' in the cotangent function?

Back

The parameter 'd' in the cotangent function y = a cot(bx + c) + d shifts the graph vertically up or down.

Front

How do you find the x-intercepts of the cotangent function?

Back

The x-intercepts of the cotangent function occur where the function equals zero, which is at x = (n + 1/2)π/b, where n is an integer.