User:Timwi
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Lemma
My name is Timwi.
Proof
Self-evident.
$\Box$
Corollary
I started the following pages:
Computer science
Trigonometry
Arccosine Logarithmic Formulation |
$\arccos x = -i \map \ln {i \sqrt {1 - x^2} + x}$ |
---|---|
Arcsine Logarithmic Formulation |
$\arcsin x = -i \map \ln {\sqrt {1 - x^2} + i x}$ |
Arctangent Logarithmic Formulation |
$\arctan x = \dfrac 1 2 i \map \ln {\dfrac {1 - i x} {1 + i x} }$ |
Area of Triangle in Terms of Two Sides and Angle |
$\map {\operatorname {Area} } {ABC} = \dfrac 1 2 a b \sin \theta$ |
Euler's Cosine Identity |
$\cos x = \dfrac {e^{i x} + e^{-i x} } 2$ |
Hyperbolic Cosine in terms of Cosine |
$\map \cos {i x} = \cosh x$ |
Cosine of Sum/Proof using Exponential Formulation |
$\map \cos {a + b} = \cos a \cos b - \sin a \sin b$ |
Hyperbolic Cosine Function is Even |
$\map \cosh {-x} = \cosh x$ |
Hyperbolic Sine Function is Odd |
$\map \sinh {-x} = -\sinh x$ |
Hyperbolic Tangent Function is Odd |
$\map \tanh {-x} = -\tanh x$ |
Euler's Sine Identity |
$\sin x = \dfrac 1 2 i \paren {e^{-i x} - e^{i x} }$ |
Hyperbolic Sine in terms of Sine |
$\map \sin {i x} = i \sinh x$ |
Sine of Sum/Proof using Exponential Formulation |
$\map \sin {a + b} = \sin a \cos b + \cos a \sin b$ |
Euler's Tangent Identity |
$\tan x = i \dfrac {1 - e^{2 i x} } {1 + e^{2 i x} }$ |
Hyperbolic Tangent in terms of Tangent |
$\map \tan {i x} = i \tanh x $ |