Understanding the Cotangent Function

The video tutorial explains the graph of the cotangent function, highlighting its relationship with the tangent function. It covers the use of similar triangles to understand cotangent, demonstrates graphing techniques both manually and with a calculator, and summarizes the key properties of the cotangent graph, including its period, domain, range, and symmetry.

What is the relationship between the cotangent and tangent functions?

• They are unrelated functions.

• They are reciprocal functions.

• They are inverse functions.

• They are identical functions.

What happens to the cotangent segment at 0 degrees or 0 radians?

• It becomes negative.

• It becomes zero.

• It becomes undefined.

• It becomes infinite.

How can the cotangent function be graphed by hand?

• By using the cosine function.

• By using the secant function.

• By using the sine function.

• By using the reciprocal of the tangent function.

What is the period of the cotangent function?

• 2π radians

• π radians

• 3π/2 radians

• π/2 radians

How can a graphing calculator be used to visualize the cotangent function?

• By entering the secant function.

• By entering the sine function.

• By entering the cosine function.

• By entering the reciprocal of the tangent function.

What is the domain of the cotangent function?

• All real numbers except multiples of π radians.

• All real numbers except multiples of π/2 radians.

• All real numbers.

• All real numbers except multiples of 2π radians.

What is the range of the cotangent function?

• 0 to 1

• -1 to 1

• Negative infinity to positive infinity

• 0 to infinity

Where do the x-intercepts of the cotangent function occur?

• At multiples of 2π radians

• At odd multiples of π/2 radians

• At even multiples of π/2 radians

• At multiples of π radians

What is the symmetry of the cotangent function?

• It has no symmetry.

• It is an even function.

• It is an odd function.

• It is symmetric about the y-axis.

What is the significance of vertical asymptotes in the cotangent function?

• They indicate where the function is zero.

• They indicate where the function is undefined.

• They indicate where the function is minimum.

• They indicate where the function is maximum.