Question

Can someone please help me with this!!

Answer 1

Explanation:

(-5, - 12) lies on the terminal side of angle
`\theta`

`\therefore \: ( - 5 \: - 12) = (x \: y) \\ r = \sqrt{ {x}^(2) + {y}^(2) } \\ = \sqrt{ {( - 5)}^(2) + {( - 12)}^(2) } \\ = √(25 + 144) \\ = √(169) \\ r= 13 \\ \\ \sin \theta = (y)/(r) = - (12)/(13) \\ \\ \cos \theta = (x)/(r) = - (5)/(13) \\ \\ \tan \theta = (y)/(x) = ( - 12)/( - 5) = (12)/(5) \\ \\ \csc \theta = (r)/(y) = - (13)/(12) \\ \\ \sec \theta = (r)/(x) = - (13)/(5) \\ \\ \cot \theta = (x)/(y) = ( - 5)/( - 12) = (5)/(12)`