In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

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$\sin(ix) = i \text{sinh}\ x$ $\cos(ix) = \text{cosh}\ x$ $\tan(ix) = i \text{tanh}\ x$ $\csc(ix) = -i \text{csch}\ x$ $\sec(ix) = \text{sech}\ x$ $\cot(ix) = -i \text{coth}\ x$ $\text{sinh}(ix) = i \sin x$ $\text{cosh}(ix) = \cos x$ $\text{tanh}(ix) = i \tan x$ $\text{csch}(ix) = -i \csc x$ $\text{sech}(ix) = \sec x$ $\text{coth}(ix) = -i \cot x$

From sinh and cosh we can create: tanh (x) = sinh (x) cosh (x) = ex − e-x ex + e-x. coth (x) = cosh (x) sinh (x) = ex + e-x ex − e-x. sech (x) = 1 cosh (x) = 2 ex + e-x. csch (x) = 1 sinh (x) = 2 ex − e-x. Why the Word "Hyperbolic" ? Because it comes from measurements made on a Hyperbola:

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Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.

Jun 25, 2024 · Tanh 是双曲正切函数，是三角学中普遍使用的 Tan 圆函数的双曲类比. Tanh[α] 定义为对应的双曲正弦和双曲余弦函数的比值，即 via . Tanh 也可以定义为 ，其中 是自然对数 Log 的底数. 当变量是有理数的（自然）对数时，Tanh 会自动计算出精确值.

cos z = tan z = with csc z, sec z, cot z as their respective reciprocals. HYPERBOLIC FUNCTIONS . From the analogy, we define the new functions known as Hyperbolic functions and csc hx, sec hx, cot hx are their reciprocals respectively. Relation between circular and hyperbolic functions. We have sin q = \ sin(ix) =

In basic trigonometry computes sine, cosine, tangent, and their reciprocal. Calculates arcsin, arccos, and arctan values inside inverse trigonometric equations. Trigonometric identities solves extremely difficult trigonometric problems. Conversions of Angles converts radian to degree scale.

Mathematically, tan function is written as f (x) = tan x. Further in this article, we will explore the tangent function graph, its domain and range, the trigonometric identities of tan x, and the formula of the tangent function. We will also solve some examples related to the tan function for a better understanding of the concept.