Question
If $\sin \theta=\frac{8}{17}$, find the other five trigonometric ratios.
✓
Answer
$\sin \theta=\frac{8}{17}=\frac{\text { Perpendicular }}{\text { Hypotenuse }} $
Base
$=\sqrt{(\text { Hypotenuse })^2-(\text { Perpendicular })^2} $
$=\sqrt{17^2-8^2} $
$=\sqrt{225} $
$=15 $
$\cos \theta=\frac{\text { Base }}{\text { Hypotenuse }}=\frac{15}{17} $
$\tan \theta=\frac{\text { Perpendicular }}{\text { Base }}=\frac{8}{15} $
$\operatorname{cosec} \theta=\frac{1}{\sin \theta}=\frac{17}{8} $
$\sec \theta=\frac{1}{\cos \theta}=\frac{17}{15} $
$\cot \theta=\frac{1}{\tan \theta}=\frac{15}{8} .$
Base
$=\sqrt{(\text { Hypotenuse })^2-(\text { Perpendicular })^2} $
$=\sqrt{17^2-8^2} $
$=\sqrt{225} $
$=15 $
$\cos \theta=\frac{\text { Base }}{\text { Hypotenuse }}=\frac{15}{17} $
$\tan \theta=\frac{\text { Perpendicular }}{\text { Base }}=\frac{8}{15} $
$\operatorname{cosec} \theta=\frac{1}{\sin \theta}=\frac{17}{8} $
$\sec \theta=\frac{1}{\cos \theta}=\frac{17}{15} $
$\cot \theta=\frac{1}{\tan \theta}=\frac{15}{8} .$
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