Question

If $\sin A=\frac{8}{17}$, find the other trigonometric ratios of $A$.

Answer 1

$\sin A=\frac{8}{17}=\frac{Perpendicular}{Hypotenuse}$

$Bas{e}^2=(Hypotenuse{)}^2-(Perpendicular{)}^2$

$Bas{e}^2={17}^2-8^2$

$Bas{e}^2=289-64$

$Bas{e}^2=225$

$Base=15$

$\cos A=\frac{Base}{Hypotenuse}=\frac{15}{17}$

$\tan A=\frac{Perpendicular}{Base}=\frac{8}{15}$

$\cot A=\frac{1}{\tan A}=\frac{15}{8}$

$\sec A=\frac{1}{\cos A}=\frac{17}{15}$

$cosecA=\frac{1}{\sin A}=\frac{17}{8}$.