Question

Given point (12,-9) how do you find the distance of the point from the origin, then find the measure of the angle in standard position whose terminal side contains the point?

Answer 1

`r = 15, angle xOP = 2 pi - arctan frac{3}{4}`

Explanation:

The old and good formulas.

`x = r cos t = 12`
`y = r sin t = -9`

`x^2 + y^2 = r^2 = 144 + 81 = 225`
`r = 15`

`y / x = tan t = -9/12 = -3/4`

`t = - arctan 0.75`

`tan(-theta) = - tan theta = tan (2 pi - theta)`