Answer
$\sin$ A = $\frac{3}{5}$
$\cos$ A = $\frac{4}{5}$
$\tan$ A = $\frac{3}{4}$
$\csc$ A = $\frac{5}{3}$
$\sec$ A = $\frac{5}{4}$
$\cot$ A = $\frac{4}{3}$
Work Step by Step
A good way to remember Trig. Functions is through the following:
SOH
CAH
TOA
In the case for this problem, angle A will be examined.
$\sin$ A = $\frac{Opposite A}{Hypotenuse}$
$\sin$ A = $\frac{24}{40}$ = $\frac{3}{5}$
$\cos$ A = $\frac{Adjacent A}{Hypotenuse}$
$\cos$ A = $\frac{32}{40}$ = $\frac{4}{5}$
$\tan$ A = $\frac{Opposite A}{Adjacent A}$
$\tan$ A = $\frac{24}{32}$ = $\frac{3}{4}$
Now, the other three Trig. Functions are the inverse of the three fundamental Trig. Functions above, and are as follows:
$\csc$ A = $\frac{Hypotenuse}{Opposite A}$
$\csc$ A = $\frac{40}{24}$ = $\frac{5}{3}$
$\sec$ A = $\frac{Hypotenuse}{Adjacent A}$
$\sec$ A = $\frac{40}{32}$ = $\frac{5}{4}$
$\cot$ A = $\frac{Adjacent A}{Opposite A}$
$\cot$ A = $\frac{32}{24}$ = $\frac{4}{3}$