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--- cubloc:tan_tanh:index [2026/02/16 05:49] – created - external edit 127.0.0.1
+++ cubloc:tan_tanh:index [2026/02/20 15:37] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
 ====== Tan ======
-Returns the sine of a number.  The Cubloc uses radians as units. Use a ''Single'' for the most precise results.
+The Tan function returns the tangent of a numeric value.
+Tangent is a fundamental trigonometric function that represents the ratio between the opposite side and the adjacent side ($\frac{opposite}{adjacent}$) of a right triangle for a given angle. It is widely used in calculations involving slopes, camera perspectives in graphics, and various engineering applications where angular ratios are required.
+On the Cubloc platform, all trigonometric functions—including Tan—use **radians** to measure angles.
+For the highest degree of precision, especially when calculating steep slopes or rapid transitions, it is recommended to use the ''Single'' data type for the input value.
+Tan accepts any real number as an angle (except for values where the cosine is zero, such as $\frac{\pi}{2}, \frac{3\pi}{2}$, etc.) and returns the corresponding tangent ratio.
+Example
 <code xbasic>
-A=Tan B   ' Return the tangent of B.
+Dim A As Single
+Dim B As Single
+B = 0.785398     ' 45 degrees in radians (PI / 4)
+A = Tan(B)       ' Returns the tangent of B (approx. 1.0)
 </code>
+==== Explanation: ====
+  * **B** should contain an angle expressed in radians. (To convert degrees to radians: $rad = deg \times \frac{\pi}{180}$)
+  * **Tan B** calculates the tangent of that angle.
+  * The resulting value—often used for gradient calculations or mapping angular movement to linear coordinates—is stored in **A**.
 ====== Tanh ======
-Returns the hyperbolic tangent of a number.  The Cubloc uses radians as units. Use a ''Single'' for the most precise results.
+The Tanh function returns the hyperbolic tangent of a numeric value.
+Unlike the standard tangent function used in circular geometry, the hyperbolic tangent is based on the geometry of a hyperbola. It is a crucial function in fields such as neural networks (as an activation function), statistics, and control systems where values need to be smoothly mapped or "squashed" into a specific range.
+On the Cubloc platform, hyperbolic functions—including Tanh—use **radians** as the unit for the input value.
+For the most accurate results, particularly when used in recursive algorithms or signal processing, the ''Single'' data type is recommended.
+One of the most important characteristics of Tanh is that it always returns a value in the range of **-1.0 to +1.0**, regardless of how large or small the input is.
+Example
 <code xbasic>
-A=Tanh B   ' Return the hyperbolic tangent of B.
+Dim A As Single
+Dim B As Single
+B = 0.5
+A = Tanh(B)      ' Returns the hyperbolic tangent of B
 </code>
+==== Explanation: ====
+  * **B** represents a real number, often serving as an input to a sigmoid-like curve.
+  * **Tanh B** computes the hyperbolic tangent using the exponential definition: $$\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
+  * The resulting value—guaranteed to be between -1.0 and 1.0—is stored in **A**, making it ideal for normalizing data or creating smooth transition thresholds.
+[[cubloc:index#system_library:|Go CUBLOC home]]

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