Precalculus Concepts for AP Calculus AB and BC

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Trigonometric Values for Common Angles

$\theta$	$\sin \theta$	$\cos \theta$	$\tan \theta$
$0$	$0$	$1$	$0$
$\frac{\pi}{6}$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{3}}$
$\frac{\pi}{4}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$1$
$\frac{\pi}{3}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$
$\frac{\pi}{2}$	$1$	$0$	$\infty$

$\sin^2 \theta + \cos^2 \theta = 1$

$1 + \tan^2 \theta = \sec^2 \theta$

$1 + \cot^2 \theta = \csc^2 \theta$

$\sin 2x = 2 \sin x \cos x$

$\cos 2x = \cos^2 x - \sin^2 x = 1 - 2 \sin^2 x$

$\ln N = p \iff e^p = N$

$\ln e = 1, \quad \ln 1 = 0$

$\ln(MN) = \ln M + \ln N$

$\ln \left(\frac{M}{N}\right) = \ln M - \ln N$

$p \cdot \ln M = \ln M^p$

The following are some common graphs that appear frequently in Precalculus and Calculus: