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Chapter 5: Problem 8

Evaluate the expression without using a calculator. \(\operatorname{arccot}(-\sqrt{3})\)

Short Answer

Expert verified
\(\operatorname{arccot}(-\sqrt{3})\) equals 150掳 or \(\frac{5\pi}{6}\) radians.

Step by step solution

01

Analyzing the input

It's known that \(\operatorname{arccot}\) function is the inverse of the cotangent function. It takes a number \(-\sqrt{3}\) as input and outputs an angle whose cotangent is that number.
02

Connecting with the unit circle

The cotangent of an angle in the unit circle is defined as the ratio of the x-coordinate to the y-coordinate. It's noticed that the cotangent of the angle 150掳 or \(\frac{5\pi}{6}\) radians is \(-\sqrt{3}\), and the same for the angle 330掳 or \(\frac{11\pi}{6}\) radians. However, \(\operatorname{arccot}\) function returns the minor positive angle that cotangent equals to the input number, but as the input number is negative, the reference angle will be in the second quadrant.
03

Evaluating the expression

Therefore, \(\operatorname{arccot}(-\sqrt{3})\) is equal to the angle 150掳 or \(\frac{5\pi}{6}\) radians.

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