Lesson 21 Graphing Tangent and Cotangent Functions

Front

What is the tangent function?

Back

The tangent function, denoted as tan(x), is a trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle. It can also be expressed as tan(x) = sin(x)/cos(x).

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) = 1/tan(x) = cos(x)/sin(x).

Front

What is the period of the tangent function?

Back

The period of the tangent function is π radians (or 180 degrees). This means that the function repeats its values every π radians.

Front

What is the period of the cotangent function?

Back

The period of the cotangent function is also π radians (or 180 degrees), similar to the tangent function.

Front

How do you graph the tangent function?

Back

To graph the tangent function, plot points for key angles (like 0, π/4, π/2, etc.), noting that it has vertical asymptotes at odd multiples of π/2.

Front

How do you graph the cotangent function?

Back

To graph the cotangent function, plot points for key angles (like 0, π/4, π/2, etc.), noting that it has vertical asymptotes at integer multiples of π.

Front

What are vertical asymptotes in tangent and cotangent functions?

Back

Vertical asymptotes occur where the function is undefined. For tan(x), they occur at x = (2n+1)π/2, and for cot(x), at x = nπ, where n is an integer.

Front

What is the range of the tangent function?

Back

The range of the tangent function is all real numbers (-∞, ∞).

Front

What is the range of the cotangent function?

Back

The range of the cotangent function is also all real numbers (-∞, ∞).

Front

What is the x-intercept of the tangent function?

Back

The x-intercept of the tangent function occurs at x = nπ, where n is an integer.