Respuesta :
Answer:
Sin θ = [tex]\frac{-15}{17}[/tex] and [tex]\frac{8}{17}[/tex].
Step-by-step explanation:
Given : cot θ = -8/15.
To find : sin θ and cos θ.
Solution : We have given
cot θ = [tex]\frac{-8}{15}[/tex].
cot θ = [tex]\frac{adjacent}{opposite}[/tex].
[tex]\frac{adjacent}{opposite}[/tex] = [tex]\frac{8}{-15}[/tex].
Hypotenuse = [tex]\sqrt{opposite^{2} +adjacent^{2} }[/tex]
Hypotenuse = [tex]\sqrt{(-15)^{2} + (8)^{2} }[/tex] .
Hypotenuse = [tex]\sqrt{225 + 64 }[/tex] .
Hypotenuse = [tex]\sqrt{289 }[/tex] .
Hypotenuse =17 .
Sin θ = [tex]\frac{opposite}{Hypotenuse}[/tex].
Plugging the values.
Sin θ = [tex]\frac{-15}{17}[/tex].
Cos θ = [tex]\frac{adjacent}{Hypotenuse}[/tex].
Cos θ = [tex]\frac{8}{17}[/tex].
Therefore, Sin θ = [tex]\frac{-15}{17}[/tex] and [tex]\frac{8}{17}[/tex].
