GRE Study Precalc

Question	Answer
$\log_{b} x = y$ means...	$b^{y} = x$
$\log_{b} (x_{1}x_{2}) =$	$\log_{b} (x_{1}) + \log_{b} (x_{2})$
$\log_{b} (x_{1}/x_{2}) =$	$\log_{b} (x_{1}) - \log_{b} (x_{2})$
$b^{\log_{b} x} =$	$x$
$(\log_{a} b)(\log_{b} x) =$	$\log_{a} x$
$\log_{b} x^{n} =$	$n\log_{b} x$
Sine/Cosine Identity	$\sin^{2} x + \cos^{2} x = 1$
Cotangent/Cosecant Identity	$1 + \cot^{2}x = \csc^{2}x$
Tangent/Secant Identity	$\tan^{2} x + 1 = \sec^{2} x$
$\sin (\alpha + \beta) =$	$\sin\alpha\cos\beta + \cos\alpha\sin\beta$
$\sin (\alpha - \beta) =$	$\sin\alpha\cos\beta - \cos\alpha\sin\beta$
$\cos(\alpha + \beta) =$	$\cos\alpha\cos\beta - \sin\alpha\sin\beta$
$\cos(\alpha - \beta) =$	$\cos\alpha\cos\beta + \sin\alpha\sin\beta$
$\tan(\alpha + \beta) =$	$\frac{\tan\alpha + \tan\beta}{1-\tan\alpha\tan\beta}$
$\tan(\alpha - \beta) =$	$\frac{\tan\alpha - \tan\beta}{1+\tan\alpha\tan\beta}$
$\sin 2\theta =$	$2\sin\theta\cos\theta$
$\cos 2\theta =$	$\cos^{2}\theta - \sin^{2}\theta$
$\tan 2\theta =$	$\frac{2\tan\theta}{1-\tan^{2}\theta}$
$\sin\frac{\theta}{2} =$	$\sqrt{\frac{1-\cos\theta}{2}}$
$\cos\frac{\theta}{2} =$	$\sqrt{\frac{1+\cos\theta}{2}}$
$\tan\frac{\theta}{2} =$	$\frac{\sin\theta}{1 + \cos\theta}$
Sum of Roots of a Polynomial	$-\frac{a_{n-1}}{a_{n}}$
Product of Roots of a Polynomial	$(-1)^{n}\frac{a_{0}}{a_{n}}$

Resource summary

	Created by Marissa Miller over 9 years ago