How to find the exact value of cotangent of pi/3?

Introduction

When dealing with trigonometry, finding exact values can be crucial. Calculating the cotangent of π/3 (pi/3) is no exception. In this article, we will explore the steps to determine this exact value and provide answers to common questions related to this topic.

The Exact Value of Cotangent of π/3

To find the exact value of cotangent π/3, we need to recall the relationship between cotangent and tangent. The cotangent of an angle is the reciprocal of its tangent value. Therefore, we can use the tangent of π/3 to determine the cotangent.

The tangent of π/3 is √3/3. Taking the reciprocal of this value will give us the cotangent. Therefore, the exact value of cotangent of π/3 is 3/√3. However, to simplify this further, we multiply both the numerator and denominator by √3 to rationalize the denominator:

How to find the exact value of cotangent of π/3?

The exact value of the cotangent of π/3 is **√3**.

By rationalizing the denominator of 3/√3, we multiply both the numerator and denominator by √3, resulting in √3 * (√3/√3) = 3/√3 = √3.

Frequently Asked Questions

1. What is the relationship between cotangent and tangent?

The cotangent of an angle is the reciprocal of its tangent value.

2. How do you find the cotangent of any angle?

To find the cotangent of any angle, take the reciprocal of its tangent value.

3. What is the tangent of π/3?

The tangent of π/3 is √3/3.

4. How do you rationalize the denominator?

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator.

5. What is the conjugate of √3?

The conjugate of √3 is √3.

6. Why rationalize the denominator?

Rationalizing the denominator simplifies the expression and allows for easier comparisons and calculations.

7. Can the value of cotangent π/3 be simplified further?

No, the value √3 is already in its simplest form.

8. How do you calculate the tangent of π/3?

To calculate the tangent of π/3, divide the length of the side opposite the angle by the length of the adjacent side in a right triangle.

9. What is the adjacent side of π/3 in a right triangle?

The adjacent side of π/3 in a right triangle is 1.

10. What is the opposite side of π/3 in a right triangle?

The opposite side of π/3 in a right triangle is √3.

11. What is the hypotenuse of π/3 in a right triangle?

The hypotenuse of π/3 in a right triangle is 2.

12. Can the cotangent of π/3 be expressed as a decimal?

Yes, the decimal approximation for the cotangent of π/3 is approximately 1.732.

Dive into the world of luxury with this video!