Cos(θ) < 0, so we know it would be in Quadrant 2 or 3
then csc(θ) = 257, but csc(θ) = [tex] \frac{1}{sin(θ)} [/tex] = 257
==> sin(θ) = [tex] \frac{1}{257} [/tex]
it is positive, so now we can determine that is in Quadrant 2
sin(θ) = opp./hyp both of opp and hyp are positive but adj suppose to negative because that way it leads the cos(θ) < 0
cos(θ) = adj/hyp
Pythereom to find the adj: [tex]257^{2} - 1^{2} = adj ==\ \textgreater \ adj \sqrt{ 257^{2} - 1^{2} } ==\ \textgreater \ adj = 16 \sqrt{258} [/tex]
cosθ = [tex] \frac{16 \sqrt{258} }{257}
[/tex]
tanθ = [tex] \frac{1}{16 \sqrt{258} } [/tex]
cosθ = [tex] 16 \sqrt{258} [/tex]
