ANSWER
[tex]\sin( \theta) = - \frac{15}{17} [/tex]
[tex]\csc( \theta) = - \frac{17}{15} [/tex]
[tex]\cos( \theta) = \frac{8}{17} [/tex]
[tex]\sec( \theta) = \frac{17}{8} [/tex]
[tex]\tan( \theta) = - \frac{15}{8} [/tex]
[tex]\cot( \theta) = - \frac{8}{15} [/tex]
EXPLANATION
From the Pythagoras Theorem, the hypotenuse can be found.
[tex] {h}^{2} = 1 {5}^{2} + {8}^{2} [/tex]
[tex] {h}^{2} = 289[/tex]
[tex]h = \sqrt{289} [/tex]
[tex]h = 17[/tex]
The sine ratio is negative in the fourth quadrant.
[tex] \sin( \theta) = - \frac{opposite}{hypotenuse} [/tex]
[tex]\sin( \theta) = - \frac{15}{17} [/tex]
The cosecant ratio is the reciprocal of the sine ratio.
[tex]\csc( \theta) = - \frac{17}{15} [/tex]
The cosine ratio is positive in the fourth quadrant.
[tex]\cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos( \theta) = \frac{8}{17} [/tex]
The secant ratio is the reciprocal of the cosine ratio.
[tex]\sec( \theta) = \frac{17}{8} [/tex]
The tangent ratio is negative in the fourth quadrant.
[tex]\tan( \theta) = - \frac{opposite}{adjacent} [/tex]
[tex]\tan( \theta) = - \frac{15}{8} [/tex]
The reciprocal of the tangent ratio is the cotangent ratio
[tex]\cot( \theta) = - \frac{8}{15} [/tex]
Answer:
sin=-15/17
cos=8/7
tan=-15/8
csc=-17/15
sec=17/8
cot=-8/15
