12 Graphs & Properties of tan, cot, sec, csc

Front

What is the domain of the tangent function?

Back

The domain of the tangent function is all real numbers except multiples of π/2.

Front

What is the equation of the tangent function with a vertical stretch of 1/2 and a horizontal compression of 2?

Back

The equation is y = (1/2)tan(2x).

Front

What is the domain of the cotangent function?

Back

The domain of the cotangent function is all real numbers except odd multiples of π/4.

Front

What is the equation of the secant function with a vertical stretch of 3 and a horizontal compression of 1/3?

Back

The equation is y = 3sec(x/3).

Front

What is the equation of the cotangent function with a horizontal compression of 2?

Back

The equation is y = cot(2x).

Front

What are the key properties of the tangent function?

Back

The tangent function is periodic with a period of π, has vertical asymptotes at odd multiples of π/2, and is undefined at these points.

Front

What are the key properties of the cotangent function?

Back

The cotangent function is periodic with a period of π, has vertical asymptotes at integer multiples of π, and is undefined at these points.

Front

What is the range of the secant function?

Back

The range of the secant function is (-∞, -1] ∪ [1, ∞).

Front

What is the range of the cosecant function?

Back

The range of the cosecant function is (-∞, -1] ∪ [1, ∞).

Front

How do you find the vertical asymptotes of the tangent function?

Back

Vertical asymptotes of the tangent function occur at x = (π/2) + nπ, where n is any integer.