Question

Find the six trigonometric ratios of the angle $\theta$ in the right triangle $ABC$, as shown at right

Answer 1

From the Fig, the opposite $side=3$, the adjacent side $=4$ and the hypotenuse $=5$.
$\sin \theta =\frac{BC}{AC}=\frac{3}{5}cosec\theta =\frac{AC}{BC}=\frac{5}{3}$
$\cos \theta =\frac{AB}{AC}=\frac{4}{5}\sec \theta =\frac{AC}{AB}=\frac{5}{4}$
$\tan \theta =\frac{BC}{AB}=\frac{3}{4}\cot \theta =\frac{AB}{BC}=\frac{4}{3}$