Question #9c537

1 Answer
Nghi N
Mar 1, 2017

#- 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#

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