Answer:
csc Θ = [tex]\frac{17}{15}[/tex]
Step-by-step explanation:
Given
tan Θ = - [tex]\frac{15}{8}[/tex] = [tex]\frac{opposite}{adjacent}[/tex] ← of a right triangle , then
hypotenuse h² = 15² + 8² = 225 + 64 = 289 ( square root both sides )
h = [tex]\sqrt{289}[/tex] = 17
Using the identity
csc x = [tex]\frac{1}{sinx}[/tex]
sin Θ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{15}{17}[/tex]
Since Θ is in second quadrant then sinΘ and csc Θ > 0, thus
csc Θ = [tex]\frac{1}{\frac{15}{17} }[/tex] = [tex]\frac{17}{15}[/tex]
