The point (-8,3) lies on the terminal arm of angle theta in standard position. Determine the primary trigonometric ratios for angle theta and calculate the value of theta to the nearest degree.

Question

Only the sine ratio was positive, and when I used that to calculate the angle, it worked, but the other ratios got different answers.

Answer 1

by Pythagoras you should have found r to be √73

so sinØ = 3/√73
cosØ = -8/√73
tanØ = -3/8

If you want to test your answers using your calculator you must consider the CAST rule

Calculators are programmed to give you the answer which is "closest" to the origin of rotation.
e.g. arctan (-3/8) gives us -20.556° which is coterminal with 360 - 20.556 or 339.44

so our angle is in II so it would be 180-20.556 or 159.444°
Check my answers with that angle, they are correct.

Answer 2

(-24,-7)