Category:Weierstrass Substitution

This category contains pages concerning Weierstrass Substitution:

The Weierstrass Substitution is an application of Integration by Substitution.

The substitution is:

$u \leftrightarrow \tan \dfrac \theta 2$

for $-\pi < \theta < \pi$, $u \in \R$.

It yields:

Sine

$\sin \theta = \dfrac {2 u} {1 + u^2}$

Cosine

$\cos \theta = \dfrac {1 - u^2} {1 + u^2}$

Derivative

$\dfrac {\d \theta} {\d u} = \dfrac 2 {1 + u^2}$