Michael J. answered • 04/14/16
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Effective High School STEM Tutor & CUNY Math Peer Leader
First, find the angle formed by the coordinate point using vector methods. To find the angle, take the inverse tangent of 7/6.
θ = tan-1(7/6)
= 49.40
This is the reference angle. To find the terminal angle, add the reference to angle to 90 degrees because the given point lies on the 2nd quadrant.
Terminal angle = 90 + 49.40
= 139.40
cot(139.40) = 1 / tan(139.40)
I will let you finish up here.
Michael J.
Which is why when the student calculates tan(139.40) on a calculator, the solution will come up negative. So overall, the solution will be negative.
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04/14/16
Kenneth S.
A more straightforward way is not to use calculator--as my answer outlined.
Using calculator, one should do tan-1(-7/6) and the result will be a 4th quadrant angle since the range of the inverse tangent function is defined (in degrees) as (-90,90). Then one should add 180 to get the correct answer in Quadrant II, consistent with the stated coordinates of the terminal side of the angle. But this calculator-based method has the demerit of not being exact.
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04/14/16
Kenneth S.
04/14/16