Answer
$\sin\theta=\dfrac{3}{5}$
$\cos\theta=\dfrac{4}{5}$
$\tan\theta=\dfrac{3}{4}$
$\cot\theta=\dfrac{4}{3}$
$\sec\theta=\dfrac{5}{4}$
$\csc\theta=\dfrac{5}{3}$
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:
$o=3$
$a=4$
Determine the hypotenuse, using the Pythagorean Theorem:
$h^2=o^2+a^2$
$h^2=3^2+4^2$
$h^2=25$
$h=\pm\sqrt{25}$
$h=\pm5$
Since $h$ is never negative, then $h=5$.
Determine the $6$ trigonometric functions of angle $\theta$:
$\sin\theta=\dfrac{o}{h}=\dfrac{3}{5}$
$\cos\theta=\dfrac{a}{h}=\dfrac{4}{5}$
$\tan\theta=\dfrac{o}{a}=\dfrac{3}{4}$
$\cot\theta=\dfrac{a}{o}=\dfrac{4}{3}$
$\sec\theta=\dfrac{h}{a}=\dfrac{5}{4}$
$\csc\theta=\dfrac{h}{o}=\dfrac{5}{3}$
