Question

In a $\Delta$ ABC, right angled at A, if $AB=12,AC=5$ and $BC=13,$find all the six trigonometric ratios of angle B.

Answer 1

with reference to $\angle B$, we have
Base = AB = 12, Perpendicular = AC = 5 and,
Hypotenuse = BC = 13
Using the definitions of trigonometric ratios, we have
$sinB=\frac{AC}{BC}=\frac{5}{13}$
$cosB=\frac{AB}{BC}=\frac{12}{13}$
$tanB=\frac{AC}{AB}=\frac{5}{12}$
$cosecB=\frac{BC}{AC}=\frac{13}{5}$
$secB=\frac{BC}{AB}=\frac{13}{12}$
and $cotB=\frac{AB}{AC}=\frac{12}{5}$