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How do you evaluate #cot300°#?

Answer 1

#cot(300^o) = - 1/sqrt(3)#

#300^o# is equivalent to #-60^o#

A #60^o# angle is one of the standard triangle angles with sides as indicated below:
cot = #("adjacent side")/("opposite side")#

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Answer 2

Dylan Arnold

Find cot 300

cot 300 = cot (120 + 180) = cot 120

Trig table gives -> # cot 120 = - (sqrt3)/3#

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Answer 3

Carter Anderson

To evaluate ( \cot(300^\circ) ), you can use the unit circle or the periodicity properties of the cotangent function:

Convert ( 300^\circ ) to its equivalent angle within one full revolution. ( 300^\circ ) is equivalent to ( 300^\circ - 360^\circ = -60^\circ ) within one full revolution.
Since the cotangent function has a period of ( 180^\circ ), you can evaluate ( \cot(-60^\circ) ) instead.
The cotangent function is defined as the reciprocal of the tangent function. The tangent of ( -60^\circ ) is ( \tan(-60^\circ) = -\sqrt{3} ) (using the unit circle or reference angles).
Therefore, ( \cot(-60^\circ) = \frac{1}{\tan(-60^\circ)} = \frac{1}{-\sqrt{3}} = -\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3} ).

Thus, ( \cot(300^\circ) = -\frac{\sqrt{3}}{3} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.