Question

Question #9c537

Answer 1

`- 56^@20; - 123^@80`
`236^@20; 303^@80`

Explanation:

Call M (2, -3), the point on the terminal arm. Consider the right triangle OMm with:
Vertical leg: mM = - 3
Horizontal leg: Om = 2
The hypotenuse `OM = sqrt(2^2 + 3^2) = sqrt13`
Call angle < mOM = t.
t is in Quadrant 4.
We get:
`sin t = - 3/sqrt13 = - 3/3.61 = - 0.83`
Calculator gives `t = - 56^@20`
Trig unit circle gives another t that has the same sine value (-0.832):
`t = - 180 + 56.20 = - 123^@80`.
Answers in interval `(-2pi, 0)`:
`- 56^@20` and `- 123^@80`
Answers in interval `(0, 2pi)`
`t = 180 + 56.20 = 236^@20` and
`t = 360 - 56.20 = 303^@80`