Question

How do you find the exact values of the six trigonometric function of `theta` if the terminal side of `theta` in the standard position contains the point (4,-3)?

Answer 1

Coordinates of the point on the terminal side:
x = 4 and y = -3. The point lies in Quadrant 4.
Call t the angle (arc):
`tan t = y/x = - 3/4`
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 9/16) = 16/25`
`cos t = 4/5` (because t lies in Quadrant 4)
`sin t = tan t.cos t = (-3/4)(4/5) = - 12/20 = - 3/5`
`cot = 1/tan = - 4/3`
`sec t = 1/cos = 5/4`
`csc t = 1/sin = -5/3`