Question

How do you sketch the angle whose terminal side in standard position passes through `(-9,-40)` and how do you find sin and cos?

Answer 1

`sin t = - 40/41`
`cos t = - 9/41`

Explanation:

The point (x = -9, y = -40) is on the terminal side of the angle t, that lies in Quadrant 3.
tan t = y/x = -40/-9 = 40/9
To find cos t, use trig identity:
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 1600/81) = 81/1681`
`cos t = -9/41` (because t lies in Quadrant 3).
`sin^2 t = 1 - cos^2 t = 1 - 81/1681 = 1600/1681`
`sin t = - 40/41` (because t lies in Quadrant 3)
Another way to find sin t:
`sin t = tan t.cos t = (-40/9)(-9/41) = 40/41`.