Question
If $\sin A = 0.8,$ find the other trigonometric ratios for $A.$
✓
Answer
$\sin A =0.8=\frac{8}{10}=\frac{4}{5}=\frac{\text { Perpendicular }}{\text { Hypotenuse }} $
Base
$=\sqrt{(\text { Hypotenuse })^2-(\text { Perpendicular })^2} $
$=\sqrt{5^2-4^2} $
$=\sqrt{25-16} $
$=\sqrt{9} $
$=3 $
$\cos A =\frac{\text { Base }}{\text { Hypotenuse }}=\frac{3}{5}=0.6 $
$\tan A =\frac{\text { Perpendicular }}{\text { Base }}=\frac{4}{3}=1.33 $
$\operatorname{cosec} A =\frac{1}{\sin A }=\frac{5}{4}=1.25 $
$\sec A =\frac{1}{\cos A }=\frac{5}{3}=1.66 $
$\cot A =\frac{1}{\tan A }=\frac{3}{4}=0.75$
Base
$=\sqrt{(\text { Hypotenuse })^2-(\text { Perpendicular })^2} $
$=\sqrt{5^2-4^2} $
$=\sqrt{25-16} $
$=\sqrt{9} $
$=3 $
$\cos A =\frac{\text { Base }}{\text { Hypotenuse }}=\frac{3}{5}=0.6 $
$\tan A =\frac{\text { Perpendicular }}{\text { Base }}=\frac{4}{3}=1.33 $
$\operatorname{cosec} A =\frac{1}{\sin A }=\frac{5}{4}=1.25 $
$\sec A =\frac{1}{\cos A }=\frac{5}{3}=1.66 $
$\cot A =\frac{1}{\tan A }=\frac{3}{4}=0.75$
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