Answer
$\sin\theta=\dfrac{5}{13}$
$\cos\theta=\dfrac{12}{13}$
$\tan\theta=\dfrac{5}{12}$
$\cot\theta=\dfrac{12}{5}$
$\sec\theta=\dfrac{13}{12}$
$\csc\theta=\dfrac{13}{5}$
Work Step by Step
Let's note:
$h$=the hypotenuse
$o$=the opposite side of angle $\theta$
$a$=the adjacent side of angle $\theta$
We are given:
$o=5$
$a=12$
Determine the hypotenuse, using the Pythagorean Theorem:
$h^2=o^2+a^2$
$h^2=5^2+12$
$h^2=169$
$h=\pm\sqrt{169}$
$h=\pm13$
Since $h$ is never negative, then $h=13$.
Determine the $6$ trigonometric functions of angle $\theta$:
$\sin\theta=\dfrac{o}{h}=\dfrac{5}{13}$
$\cos\theta=\dfrac{a}{h}=\dfrac{12}{13}$
$\tan\theta=\dfrac{o}{a}=\dfrac{5}{12}$
$\cot\theta=\dfrac{a}{o}=\dfrac{12}{5}$
$\sec\theta=\dfrac{h}{a}=\dfrac{13}{12}$
$\csc\theta=\dfrac{h}{o}=\dfrac{13}{5}$
