Answer:
[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Using the trigonometric identity
csc Θ = [tex]\frac{1}{sin0}[/tex]
Since Θ is in first quadrant then csc Θ > 0
Given
Θ = [tex]tan^{-1}[/tex]([tex]\frac{4}{3}[/tex]), then
tanΘ = [tex]\frac{4}{3}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
This represents a 3- 4- 5 right triangle with hypotenuse = 5, thus
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex], thus
csc Θ = [tex]\frac{1}{\frac{4}{5} }[/tex] = [tex]\frac{5}{4}[/tex]
