ANSWER
See explanation
EXPLANATION
The given triangle is a right angle triangle.
We use the mnemonics SOH CAH TOA.
The given angle is
[tex] \alpha [/tex]
The opposite is 8 units, the adjacent is 15 units and the hypotenuse is 17 units.
[tex] \sin( \alpha ) = \frac{opposite}{hypotenuse} = \frac{8}{17} [/tex]
[tex] \csc( \alpha ) = \frac{1}{ \sin( \alpha ) } = \frac{17}{8} [/tex]
[tex]\tan( \alpha ) = \frac{opposite}{adjacent} = \frac{8}{11} [/tex]
[tex] \cot( \alpha ) = \frac{1}{ \tan( \alpha ) } = \frac{15}{8} [/tex]
[tex]\cos( \alpha ) = \frac{adjacent}{hypotenuse} = \frac{15}{17} [/tex]
[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } = \frac{17}{15} [/tex]
