User:Timwi

From ProofWiki
Jump to navigation Jump to search

Lemma

My name is Timwi.

Proof

Self-evident.

$\blacksquare$

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

$\map {\operatorname {Area} } {ABC} = \dfrac 1 2 a b \sin \theta$

Cosine Exponential Formulation

$\cos x = \dfrac {e^{i x} + e^{-i x} } 2$

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

$\map \tanh {-x} = -\tanh x$

Sine Exponential Formulation

$\sin x = \dfrac 1 2 i \paren {e^{-i x} - e^{i x} }$

Hyperbolic Sine in terms of Sine

$\map \sin {i x} = i \sinh x$

Sine of Sum/Proof using Exponential Formulation

$\map \sin {a + b} = \sin a \cos b + \cos a \sin b$

Tangent Exponential Formulation

$\tan x = i \dfrac {1 - e^{2 i x} } {1 + e^{2 i x} }$

Hyperbolic Tangent in terms of Tangent

$\map \tan {i x} = i \tanh x $