Answer:
[tex]\sin \theta =\frac{-15}{17}\\cos \theta =\frac{8}{17}\\\tan \theta =\frac{-15}{8}\\\csc \theta =\frac{-17}{15}\\\sec \theta =\frac{17}{8}\\\cot \theta =\frac{-8}{15}[/tex]
Step-by-step explanation:
Given: (8,-15) is on the terminal ray of angle
To find: All the trigonometric ratios
Solution:
Trigonometry is a branch of mathematics that explain relationship between the sides and angles of triangles.
If (x, y) lies on the terminal side of θ then [tex]r=\sqrt{x^2+y^2}[/tex]
[tex]r=\sqrt{(8)^2+(-15)^2}=\sqrt{64+225}=\sqrt{289}=17[/tex] units
[tex]\sin \theta =\frac{y}{r}=\frac{-15}{17}\\cos \theta =\frac{x}{r}=\frac{8}{17}\\\tan \theta =\frac{y}{x}=\frac{-15}{8}\\\csc \theta =\frac{1}{\sin \theta }=\frac{-17}{15}\\\sec \theta =\frac{1}{cos \theta}=\frac{17}{8}\\\cot \theta =\frac{1}{\tan \theta}=\frac{-8}{15}[/tex]
