Answer:
Step-by-step explanation:
From the information given:
[tex]r^2 = x^2 +y^2[/tex]
[tex]r^2 = (-6)^2 + (5)^2[/tex]
[tex]r^2 = 36 +25[/tex]
[tex]r^2 =61[/tex]
[tex]r = \sqrt{61}[/tex]
[tex]Sin \theta = \dfrac{y}{r} = \dfrac{5}{\sqrt{61}}[/tex]
[tex]Cos \theta = \dfrac{x}{r} = \dfrac{- 6 }{\sqrt{61}}[/tex]
[tex]Sec \theta = \dfrac{1}{cos \theta} = \dfrac{\sqrt{61}}{5}[/tex]
[tex]tan \theta = \dfrac{Sin \theta }{Cos \theta}[/tex]
[tex]tan \theta = \dfrac{\dfrac{5}{\sqrt{61}} }{\dfrac{{-6} }{\sqrt{61}} }[/tex]
[tex]tan \theta = {\dfrac{5}{\sqrt{61}} }\times \dfrac{\sqrt{61} }{-6}[/tex]
[tex]tan \theta = {\dfrac{5}{-6} }[/tex]
