Given the point P(-5/13,12/13)
the angle t is
then
since we know x and y values (-5/13,12/13) we can solve theta
where
Opp = -5/13
Adj = 12/13
[tex]tan(\theta)=\frac{Opp}{Adj}[/tex][tex]tan(\theta)=\frac{\frac{-5}{3}}{\frac{12}{13}}[/tex][tex]tan(\theta)=\frac{-5*13}{3*12}[/tex][tex]tan(\theta)=\frac{-65}{36}[/tex][tex]\theta=ArcTan(\frac{-65}{36})[/tex][tex]\theta=61.02°[/tex]Adding the 90° of the first quadrant
The angle t is
[tex]t=61.02+90[/tex][tex]t=151.02[/tex]to rads
[tex]t=\frac{151.02\pi}{180}[/tex]then sin t
[tex]sin(t)=0.48450[/tex]
