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Why is the tangent function an odd function?
Which tangent function is not defined at odd multiples of /2?
Is a tangent function a discontinuous graph?
Which tangent function is differentiable at x D?
What is tangent function?
Which trigonometric function is an odd function?
Jan 30, 2015 · A function is odd if: f(-x)=-f(x). In this case: y=tan(-x)=sin(-x)/cos(-x)=(-sin(x))/cosx=-sinx/cosx=-tan(x), for the simmetry of sinus and cosinus. Trigonometry
The tangent function is an odd function because tan (-x) = -tan x. Tan x is not defined at values of x where cos x = 0. The graph of tan x has an infinite number of vertical asymptotes.
6 days ago · The definition of an odd function is that f (− x) = − f (x) for all x in the domain of the function. To prove that the tangent function is odd, we can use this definition and show that tan (− x) = − tan x for all x ≠ k π + π 2, k ∈ Z.
Therefore, tangent is an odd function. We can further analyze the graphical behavior of the tangent function by looking at values for some of the special angles, as listed in Table \(\PageIndex{1}\).
The tangent function has domain \(D\) (as defined above), range \(\mathbb{R},\) and is differentiable at every point \(x \in D .\) Moreover, the tangent function is increasing on each interval of the form \[\left(-\frac{\pi}{2}+n \pi, \frac{\pi}{2}+n \pi\right),\] \(n \in \mathbb{Z},\) with
Oct 6, 2021 · Figure \(\PageIndex{6}\): The function \(f(x)=x^3\) is an odd function. We can test whether a trigonometric function is even or odd by drawing a unit circle with a positive and a negative angle, as in Figure \(\PageIndex{7}\).
Sine, cosine, and tangent are the most widely used trigonometric functions. Their reciprocals, though used, are less common in modern mathematics. Trigonometric functions are also called circular functions. 6 trig functions. The table below shows the six trigonometric function values for the specified angles in both degrees and radians.
