Answer:
[tex]\theta = 14.1\ degrees[/tex]
[tex]846\ minutes[/tex]
Step-by-step explanation:
Given
[tex]csc(\theta) = 4.1191[/tex]
Required
Solve for [tex]\theta[/tex]
[tex]csc(\theta) = 4.1191[/tex]
[tex]csc(\theta) = \frac{1}{sin(\theta)}[/tex]
So, we have:
[tex]\frac{1}{sin(\theta)} = 4.1191[/tex]
Invert both sides
[tex]sin(\theta) = \frac{1}{4.1191}[/tex]
[tex]sin(\theta) = 0.2428[/tex]
Take [tex]sin^{-1}[/tex] of both sides
[tex]sin^{-1} sin(\theta) = sin^{-1}0.2428[/tex]
[tex]\theta = sin^{-1}0.2428[/tex]
[tex]\theta = 14.0518577574[/tex]
[tex]\theta = 14.1\ degrees[/tex] --- approximated
Convert to minutes:
[tex]1\ degree = 60\ minutes[/tex]
So:
[tex]14.1\ degrees = 14.1 * 60\ minutes[/tex]
[tex]14.1\ degrees = 846\ minutes[/tex]
