Business Mathematics and Basic Statistics · Ch 6 — Trigonometry

Ratios of Angles Beyond 90° — 120°, 135°, 150°, 180°

Each of $120°, 135°, 150°, 180°$ can be written as $180°$ minus a standard angle already in the table:

120° = 180° - 60° \qquad 135° = 180° - 45° \qquad 150° = 180° - 30° \qquad 180° = 180° - 0°

Applying the supplementary-angle rule from the previous section (sine keeps its sign, cosine and tangent flip sign) to each of these gives the extended table:

Note

Ratios Beyond 90°

$\theta$	$120°$	$135°$	$150°$	$180°$
$\sin\theta$	$\dfrac{\sqrt3}{2}$	$\dfrac{1}{\sqrt2}$	$\dfrac12$	$0$
$\cos\theta$	$-\dfrac12$	$-\dfrac{1}{\sqrt2}$	$-\dfrac{\sqrt3}{2}$	$-1$
$\tan\theta$	$-\sqrt3$	$-1$	$-\dfrac{1}{\sqrt3}$	$0$

Every entry above is read directly from the $0°$ – $90°$ table two sections back — nothing here is a new value, only a sign applied to an already-known one. …

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