Math Problem Statement

cot (-5pi/6)

Solution

The value of cot(5π/6)\cot(-5\pi/6) can be calculated as follows:

  1. Understanding the angle: 5π/6 is in the third quadrant since it’s equivalent to π(5π/6)=π/6 radians.-5\pi/6 \text{ is in the third quadrant since it's equivalent to } \pi - (-5\pi/6) = \pi/6 \text{ radians}. In the third quadrant, cotangent is positive, because cot(θ)=1tan(θ)\cot(\theta) = \frac{1}{\tan(\theta)}, and both sine and cosine are negative, making their ratio positive.

  2. Reference angle: The reference angle for 5π/6-5\pi/6 is π/6\pi/6.

  3. Cotangent of the reference angle: cot(π/6)=3\cot(\pi/6) = \sqrt{3}

  4. Sign: Since the cotangent function is positive in the third quadrant, the value of cot(5π/6)\cot(-5\pi/6) is the same as cot(π/6)\cot(\pi/6).

Thus, cot(5π/6)=3\cot(-5\pi/6) = \sqrt{3}.


Do you need further details or have any questions?

Here are five related questions:

  1. What is the value of tan(5π/6)\tan(-5\pi/6)?
  2. How do you calculate sin(5π/6)\sin(-5\pi/6)?
  3. What is the general formula for cotangent in different quadrants?
  4. Can you derive cotangent from sine and cosine?
  5. How do you convert angles between radians and degrees?

Tip: Remember that cotangent is the reciprocal of tangent, i.e., cot(θ)=1tan(θ)\cot(\theta) = \frac{1}{\tan(\theta)}.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Cotangent Function
Reference Angles
Quadrants

Formulas

cot(θ) = 1/tan(θ)
Reference angle: |θ|
cot(π/6) = √3

Theorems

Cotangent in different quadrants
Reciprocal identity of tangent and cotangent

Suitable Grade Level

Grades 10-12