SOLUTION: +++Point (-5,-3) is on the terminal arm of an angle in standard position.
(a) Sketch the principal angle
(b) What is the measure of the related acute angle to the nearest degr
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-> SOLUTION: +++Point (-5,-3) is on the terminal arm of an angle in standard position.
(a) Sketch the principal angle
(b) What is the measure of the related acute angle to the nearest degr
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Question 933308: +++Point (-5,-3) is on the terminal arm of an angle in standard position.
(a) Sketch the principal angle
(b) What is the measure of the related acute angle to the nearest degree?
(c) What is the measure of principal angle to the nearest degree?
(d) What is the measure of the first negative coterminal angle? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the angle is in the third quadrant.
the length of the opposite side is -3 and the length of the adjacent side is -5.
the tangent of the reference angle is equal to -3/-5.
the absolute value of the tangent is equal to 3/5 = .6.
the arctan of that will give you the angle in the first quadrant which is the same as the reference angle.
arctan 3/5 = arctan .6 = 30.96376 rounded to 5 decimal places.
since the angle is in the third quadrant, then the angle is equal to 180 + the reference angle which is equal to 180 + 30.96376 = 210.96376.
to find the first coterminal negative angle, subtract 360 from that angle until it goes negative.
210.96376 - 360 = -149.03624 degrees rounded to 5 decimal places.
your principal angle is 210.96376 degrees.
your smallest negative angle is -149.03624 degrees.
your reference angle is 30.96376 degrees.
see the diagram below:
in the diagram:
ra = the reference angle
pa = the primary angle
fnca = first negative coterminal angle
