Question 933308
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

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