add trig and hyperbolic trig (#12)

Author: Marcos-cat

README.md

@@ -24,6 +24,18 @@ Functions list (see in-code documentation for more detail)
 | `Median` | Median |
 | `Var` | Variance |
 | `Stdev` | Standard deviation |
+| `Sin` | Sine |
+| `Cos` | Cosine |
+| `Tan` | Tangent |
+| `Csc` | Cosecant |
+| `Sec` | Secant |
+| `Cot` | Cotangent |
+| `Sinh` | Hyperbolic sine |
+| `Cosh` | Hyperbolic cosine |
+| `Tanh` | Hyperbolic tangent |
+| `Csch` | Hyperbolic cosecant |
+| `Sech` | Hyperbolic secant |
+| `Coth` | Hyperbolic cotangent |
 | `MDet` | Matrix determinant |
 | `Mgje` | Matrix Gauss-Jordan Elimination |
 | `MCof` | Matrix cofactors |

lib.ua

@@ -26,6 +26,52 @@ Var ← -˙×∩÷∩⊃⧻/+⟜˙×
 # Standard deviation
 Stdev ← √Var
 
+# -- Trigonometry --
+
+# Sine
+Sin ← ∿
+# Cosine
+Cos ← ∿˜-η
+# Tangent
+Tan ← ⌅(÷°∠|∠⊙1)
+
+# Cosecant
+Csc ← ⨪Sin
+# Secant
+Sec ← ⨪Cos
+# Cotangent
+Cot ← Tan˜-η
+
+# Hyperbolic Sine
+Sinh ← ⌅(÷₂-∩ₑ⊸¯|°ₑ+⟜⍜˙×+₁)
+# Hyperbolic Cosine
+Cosh ← ⌅(÷₂+∩ₑ⊸¯|°ₑ+⟜⍜˙×-₁)
+# Hyperbolic Tangent
+Tanh ← ⌅(÷⊃+-1ₑ×₂|÷₂°ₑ÷˜⊃-+1)
+
+# Hyperbolic Cosecant
+Csch ← ⨪Sinh
+# Hyperbolic Secant
+Sech ← ⨪Cosh
+# Hyperbolic Cotangent
+Coth ← ⨪Tanh
+
+┌─╴test
+  # Inverse functions have standard ranges
+  ⍤⤙≍ ¯η_0_η °Sin ¯1_0_1
+  ⍤⤙≍ 0_¯η_η_0 °Csc ¯∞_¯1_1_∞
+  ⍤⤙≍ π_η_0 °Cos ¯1_0_1
+  ⍤⤙≍ η_π_0_η °Sec ¯∞_¯1_1_∞
+  ⍤⤙≍ ¯η_¯η/2_0_η/2_η °Tan ¯∞_¯1_0_1_∞
+  ⍤⤙≍ π_3η/2_η_η/2_0 °Cot ¯∞_¯1_0_1_∞
+
+  ˙⍤ /×=1 ⁅₅ -∩˙×⊃Sinh Cosh ×2-⊸¬÷⟜⇡10 # Pythagorean Identity
+
+  ⍤⤙≍ ¯0.88137_0.88137 ⁅₅ °Csch ¯1_1
+  ⍤⤙≍ ∞_1.31696_0 ⁅₅ °Sech 0_1/2_1
+  ⍤⤙≍ ¯0.54931_¯∞_∞_0.54931 ⁅₅ °Coth ¯2_¯1_1_2
+└─╴
+
 # -- Matrices/Vectors --
 
 # ? SwappedRows Pivot