# Math

When trying to solve
arctan(sqrt 567.2 / -459.6) my answer was -2.96. My teacher said that i handled the radical wrong. She said I have to square both numbers, then add them, and then find the square root. I am confused because you cannot take the square root of -459.6. Please explain.

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1. Im not sure by your equation why you are to follow that process, but if you are to first square the two numbers then you get rid of the -ve

ie:

567.2^2 and (-459.6)^2

i hope this helps

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2. arctan(sqrt 567.2 / -459.6)
= arctan(23.81596/-459.6)
= arctan(-.051819)
= -2.97°

most calculators have been programmed that for any arc(trig function) they will give you the smallest value of rotation from 0,
so -2.97 would be in the 4th quadrant, coterminal with 360-2.97 or 357.03°

the tangent is also negative in the 2nd quadrant, so
the smallest positive answer is 180-2.97 = 177.03°

check: tan 357.03 = tan 177.03 = .05188
√567.2/-459.6 = .0518189 , close enough,

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