Answer
$\sin\theta=\dfrac{15}{17}$
$\cos\theta=\dfrac{8}{17}$
$\tan\theta=\dfrac{15}{8}$
$\csc\theta=\dfrac{17}{15}$
$\sec\theta=\dfrac{17}{8}$
$\cot\theta=\dfrac{8}{15}$
Work Step by Step
The triangle is shown in the attached image below.
Let $h$ be the hypotenuse of the triangle. Use the Pythagorean Theorem to find it:
$h=\sqrt{8^{2}+15^{2}}=\sqrt{64+225}=\sqrt{289}=17$
$\sin\theta=\dfrac{opposite}{hypotenuse}=\dfrac{15}{17}$
$\cos\theta=\dfrac{adjacent}{hypotenuse}=\dfrac{8}{17}$
$\tan\theta=\dfrac{opposite}{adjacent}=\dfrac{15}{8}$
$\csc\theta=\dfrac{hypotenuse}{opposite}=\dfrac{17}{15}$
$\sec\theta=\dfrac{hypotenuse}{adjacent}=\dfrac{17}{8}$
$\cot\theta=\dfrac{adjacent}{opposite}=\dfrac{8}{15}$