Tangent & Cotangent Graphs

Front

What is the period of the function y=tan(\frac{3}{4}θ)?

Back

The period is \frac{4π}{3}.

Front

What are the vertical asymptotes for y = tan(x)?

Back

The vertical asymptotes are x = \frac{π}{2}, \frac{3π}{2}, ...

Front

Let f(x) = 3 cot(4t) - 5. What is the period of f(x)?

Back

The period is \frac{π}{4}.

Front

What is the equation of the graph shown if it is y=tan(\frac{1}{2}x)?

Back

The equation is y=tan(\frac{1}{2}x).

Front

Assuming no transformations, what type of function is y=3cot(4t)-5?

Back

The function is a Cotangent function.

Front

Define the tangent function.

Back

The tangent function, tan(θ), is defined as the ratio of the opposite side to the adjacent side in a right triangle.

Front

What is the range of the tangent function?

Back

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

Front

What is the period of the cotangent function?

Back

The period of the cotangent function is π.

Front

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

Back

Vertical asymptotes occur where the function is undefined, specifically at x = \frac{π}{2} + nπ, where n is an integer.

Front

What is the relationship between tangent and cotangent functions?

Back

The cotangent function is the reciprocal of the tangent function: cot(θ) = \frac{1}{tan(θ)}.