Business Mathematics and Statistics · Ch 4 — Trigonometry

Trigonometric Ratios of Standard Angles

The trigonometric ratios of five standard angles — $0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ$ — come up so often in problem-solving that they are worth memorising outright rather than recomputing every time.

$\theta$	$0^\circ$	$30^\circ$	$45^\circ$	$60^\circ$	$90^\circ$
$\sin\theta$	$0$	$\tfrac{1}{2}$	$\tfrac{1}{\sqrt2}$	$\tfrac{\sqrt3}{2}$	$1$
$\cos\theta$	$1$	$\tfrac{\sqrt3}{2}$	$\tfrac{1}{\sqrt2}$	$\tfrac{1}{2}$	$0$
$\tan\theta$	$0$	$\tfrac{1}{\sqrt3}$	$1$	$\sqrt3$	undefined
$\operatorname{cosec}\theta$	undefined	$2$	$\sqrt2$	$\tfrac{2}{\sqrt3}$	$1$
$\sec\theta$	$1$	$\tfrac{2}{\sqrt3}$	$\sqrt2$	$2$	undefined
$\cot\theta$	undefined	$\sqrt3$	$1$	$\tfrac{1}{\sqrt3}$	$0$

Definition 1Standard-Angle Ratio Table

The memorised values of all six ratios at $0^\circ,30^\circ,45^\circ,60^\circ,90^\circ$ , used as building blocks for compou …

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