Sketch a Tangent Functions

Answer 1

tangent graph, y = tanθ y = tan θ, for −180° ≤ θ ≤ 180° − 180 ° ≤ θ ≤ 180 ° is undefined at θ = −90° θ = − 90 ° and θ = 90° θ = 90 °. Therefore we can determine the asymptotes of f (θ) = tan

Answer 2

A tangent function is a trigonometric function that describes the ratio of the side opposite a given angle in a right triangle to the side adjacent to that angle. In other words, it describes the slope of a line tangent to a point on a unit circle. The graph of a tangent function is a periodic wave that oscillates between positive and negative values.

To sketch a tangent function, we can start by plotting points on a coordinate plane. The x-axis represents the angle in radians, and the y-axis represents the value of the tangent function. The period of the function is 2π radians, so we can plot points every 2π units on the x-axis.

The graph of the tangent function is asymptotic to the x-axis. It oscillates between positive and negative values, crossing the x-axis at π/2 and 3π/2 radians. The graph reaches its maximum value of 1 at π/4 and 7π/4 radians, and its minimum value of -1 at 3π/4 and 5π/4 radians.

In summary, the graph of the tangent function is a wave that oscillates between positive and negative values, crossing the x-axis at π/2 and 3π/2 radians, with a period of 2π radians.

Answer 3

To sketch a tangent function, follow these steps:

Determine the period of the function: The period of the tangent function is π radians or 180 degrees.

Determine the x-intercepts: The tangent function has x-intercepts at every π radians or 180 degrees. These points occur at x = π/2, 3π/2, 5π/2, etc.

Determine the vertical asymptotes: The tangent function has vertical asymptotes at every odd multiple of π/2. These points occur at x = π/2, 3π/2, 5π/2, etc.

Determine the horizontal asymptote: The tangent function has a horizontal asymptote at y = 0.

Plot the points and graph the function: Use the x-intercepts and vertical asymptotes to divide the function into intervals, and then plot a few points within each interval. Connect the points with smooth curves to complete the graph.

It's important to note that the tangent function has a rapid increase or decrease in value near its vertical asymptotes, so the graph may appear to "jump" or "bounce" near these points. Additionally, the tangent function has no maximum or minimum values, so the graph extends indefinitely in both the positive and negative y-directions.

Answer 4

I can explain what the graph of a tangent function looks like.

The graph of a tangent function is a periodic curve that oscillates between positive and negative infinity, crossing the x-axis at regular intervals. The tangent function has vertical asymptotes at odd multiples of pi/2 (where the function is undefined), and it approaches these asymptotes from both positive and negative directions.

The general form of the tangent function is f(x) = tan(x), where x is the angle in radians. As x increases, the value of tan(x) increases without bound as it approaches the vertical asymptotes. Similarly, as x decreases, the value of tan(x) approaches negative infinity as it approaches the vertical asymptotes.

The period of the tangent function is pi, which means that the function repeats itself every pi units. The tangent function is also an odd function, which means that f(-x) = -f(x). This symmetry is reflected in the graph, which is symmetric about the origin.

Overall, the graph of the tangent function is a unique and interesting curve that has many applications in trigonometry, calculus, and other areas of mathematics.

Answer 5

Sure! Here is a sketch of the tangent function, also known as the tan(x) function:

The graph of the tangent function repeats itself in a pattern with vertical asymptotes where the function approaches positive or negative infinity. It also has a period of π, meaning the pattern repeats every π units horizontally. The function oscillates between positive and negative values, crossing the x-axis at the x-values where the tangent function is equal to zero.

Please note that the graph above is a rough sketch and may not be to scale. It is recommended to use a graphing tool or software to obtain a more accurate and detailed graph of the tangent function.

Answer 6

Tangent functions are typically represented on a coordinate system known as the tangent graph or tangent curve. It is a periodic function that repeats its pattern over a specific interval. The graph consists of vertical asymptotes where the function approaches infinity and horizontal lines where the function approaches zero.

Answer 7

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Answer 8

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Answer 9

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