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      • Graph for y = tan (x) = y shows how the tangent returns a value y for the angle x (measured in radians). Tangent function is a periodic function and the period of tangent function is π radians, thus the graph of tangent function repeat itself in every π radians along the x-axis.
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  2. We can use what we know about the properties of the tangent function to quickly sketch a graph of any stretched and/or compressed tangent function of the form \(f(x)=A\tan(Bx)\).

  3. The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.

  4. The tan graph is a visual representation of the tangent function for a given range of angles. The horizontal axis of a trigonometric graph represents the angle, usually written as \theta , and the y -axis is the tangent function of that angle.

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  5. The graph of y = tan θ. As the point P moves anticlockwise round the circle, the values of \ (\cos {\theta}\) and \ (\sin {\theta}\) change, therefore the value of \ (\tan {\theta}\) will...

    • Definition and Graph of The Tangent Function
    • Properties of Tan X
    • Interactive Tutorial on Tangent Function

    We first consider angle θ with initial side on the positive x axis (in standard position) and terminal side OM as shown below. The tangent function is defined as tan(θ)=yx From the definiton of the tangent, we can use the definitions of the sin(θ) and cos(θ) to deduce a relationship between tan, sin and cos functions as follows: tan(θ)=yx=y/rx/r=si...

    1) tan x has a period equal to \pi . 2) \tan(x) has vertical asymptotes at all values of x = \dfrac{\pi}{2} + n\pi , n being any integer. 3) The domain of \tan(x) is the set of all real numbers except x = \dfrac{\pi}{2} + n\pi , n being any integer. 4) The graph of \tan(x) is symmetric with respect to the origin of the system of axes. 5) The range ...

    Set a = 1, b = 1, c = 0 and d = 0. Write down f(x) and take note of the period phase shift and positions of asymptotes (in red) of f(x)? Now change a , how does it affect the graph?
    set a = 1, c = 0, d = 0 and change b. Find the period from the graph and compare it to pi/|b| . How does b affect the graph of f(x)? How does it affect the asymptotes?
    set a = 1, b = 1, d = 0 and change c starting from zero going slowly to positive large values. Take note of the shift, is it left or right, and compare it to - c / b .
    set a = 1, b = 1, d = 0 and change c starting from zero going slowly to negative smaller values. Take note of the shift, is it left or right, and compare it to - c / b .
  6. The name of the tangent function comes from the tangent line that is perpendicular to the radius and intersects the circle at a single point. To create a tangent segment, draw a line perpendicular to the x-axis and then extend θ so it intersects the tangent line. The tangent function is defined as the length of the red segment.

  7. Jun 27, 2014 · Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig...

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