docs: add edge case tests to repl.txt for sin()

Author: ishikajais27

lib/node_modules/@stdlib/math/base/special/sin/docs/repl.txt

@@ -1,84 +1,103 @@
-    # sin(x) - Your Chill Math Buddy
-
-Hey! Sine takes an angle and gives you a number—like a height on a circle. Great for coding, music, or math fun. Let’s check it out!
-
----
-
-## What You Give It
-
-- **x**: a number  
-  Angle in radians (not degrees—a full spin’s about 6.28). Works with any number, even `NaN` or infinity.
-
-## What You Get Back
-
-- **y**: a number  
-  Between -1 and 1. `NaN` if `x` is weird.
-
-## What It’s Good For
-
-- Smooth game moves
-- Sound tweaks
-- Shape math
-
----
-__________________________________________________________________________
-## Give These a Go
-
-- `sin(0.0)` → `0.0` (no turn)
-- `sin( {{alias:@stdlib/constants/float64/pi}} / 2 )` → `1.0` (90°—top!)
-- `sin( -{{alias:@stdlib/constants/float64/pi}} / 6 )` → `-0.5` (-30° dip)
-- `sin( 0.785 )` → ~`0.707` (45°—even)
-- `sin( {{alias:@stdlib/constants/float64/pi}} )` → `0.0` (half spin)
-- `sin( Infinity )` → `NaN` (too big!)
-
----
-__________________________________________________________________________
-## Fun Code to Try
-
-### For C Folks
-code->
-- **Add**: `#include <math.h>`  
-- **Bounce a Ball**:  
-  ```c
-  #include <math.h>
-  #include <stdio.h>
-  int main() {
-      for (int step = 0; step < 5; step++) {
-          printf("Height %d: %.2f\n", step, sin(step * 0.5));
-      }
-      return 0;
-  }
-
-  gcc file.c -lm—prints 0.00, 0.48, 0.91...
-______________________________________________________________________
-### For JavaScript Folks
-Use: Math.sin()
-Fade a Light:
-code->
-for (let time = 0; time < 5; time += 0.5) {
-    let glow = (Math.sin(time) + 1) / 2;
-    console.log(`Glow ${time}: ${glow.toFixed(2)}`);
-}
-output->
-Shows 0.50, 0.73, 0.91—smooth!
-__________________________________________________________________
-Extra: Mix Waves
-code->
-let mix = Math.sin(1.5) + Math.sin(2.5);
-console.log("Wave mix:", mix.toFixed(3)); // ~ -0.589
-__________________________________________________________________
-Quick Bits
-Loops: Repeats every 6.28. sin(100) = sin(100 % 6.28).
-Flips: sin(-x) = -sin(x).
-Stays Simple: -1 to 1 only.
-Spot-On: sin(π/2) = 1, sin(0) = 0.
-___________________________________________________________________
-Easy Tips
-Degrees?: Multiply by 3.14 / 180. sin(60 * 3.14 / 180) ≈ 0.866.
-Save It: Store repeats—like let h = sin(1.5).
-Handy: sin(3.14 / 3) ≈ 0.866 (60°).
-___________________________________________________________________
-Other Pals
-cos(x): Wave teammate.
-tan(x): Slope helper.
-{{alias:@stdlib/constants/float64/pi}}: 3.14159.
+sin( x )
+    Computes the sine of a number.
+
+    Parameters
+    ----------
+    x: number
+        Input value (in radians). Can be any number, including `NaN` or `Infinity`.
+
+    Returns
+    -------
+    y: number
+        Sine of the input value, a number between -1 and 1. Returns `NaN` for invalid inputs like `NaN` or `Infinity`.
+
+    Notes
+    -----
+    - The sine function is periodic with a period of 2π (approximately 6.28 radians), so `sin(x) = sin(x % 6.28)`.
+    - The function satisfies the identity `sin(-x) = -sin(x)`.
+    - Useful for smooth game movements, sound wave adjustments, and geometric calculations.
+    - To convert degrees to radians, multiply by π/180 (e.g., `sin(60 * 3.14 / 180) ≈ 0.8660` for 60 degrees).
+    - For repeated calculations, store the result to avoid recomputing (e.g., `let h = sin(1.5)`).
+
+    Examples
+    --------
+    > var y = sin( 0.0 )
+    0.0
+
+    > y = sin( {{alias:@stdlib/constants/float64/pi}} / 2.0 )
+    1.0
+
+    > y = sin( -{{alias:@stdlib/constants/float64/pi}} / 6.0 )
+    -0.5
+
+    > y = sin( 0.7853981633974483 )
+    ~0.7071
+
+    > y = sin( {{alias:@stdlib/constants/float64/pi}} )
+    0.0
+
+    > y = sin( 2 * {{alias:@stdlib/constants/float64/pi}} )
+    0.0
+
+    > y = sin( {{alias:@stdlib/constants/float64/pi}} / 3.0 )
+    ~0.8660
+
+    > y = sin( -{{alias:@stdlib/constants/float64/pi}} )
+    0.0
+
+    > y = sin( Infinity )
+    NaN
+
+    > y = sin( NaN )
+    NaN
+
+    > y = sin( 1e308 )
+    NaN
+
+    > y = sin( -1e308 )
+    NaN
+
+    > y = sin( 1e-308 )
+    ~1e-308
+
+    > y = sin( -0.0 )
+    -0.0
+
+    > y = sin( 3 * {{alias:@stdlib/constants/float64/pi}} / 2.0 )
+    -1.0
+
+    > // Simulate a fading light effect:
+    > for (let time = 0; time < 5; time += 0.5) {
+    >     let glow = (sin(time) + 1) / 2;
+    >     console.log(`Glow ${time}: ${glow.toFixed(2)}`);
+    > }
+    Glow 0: 0.50
+    Glow 0.5: 0.73
+    Glow 1: 0.91
+    ...
+
+    > // Mix two sine waves:
+    > let mix = sin(1.5) + sin(2.5);
+    > mix
+    ~-0.589
+
+    > // C example to simulate a bouncing ball:
+    > // Save as `bounce.c` and compile with `gcc bounce.c -lm`
+    > #include <math.h>
+    > #include <stdio.h>
+    > int main() {
+    >     for (int step = 0; step < 5; step++) {
+    >         printf("Height %d: %.2f\n", step, sin(step * 0.5));
+    >     }
+    >     return 0;
+    > }
+    Height 0: 0.00
+    Height 1: 0.48
+    Height 2: 0.91
+    ...
+
+    See Also
+    --------
+    cos( x ): Computes the cosine, a related trigonometric function.
+    tan( x ): Computes the tangent, useful for slopes.
+    {{alias:@stdlib/constants/float64/pi}}: The constant π (approximately 3.14159).