Cot (60°) = 1/tan (60°) = 1/sqrt{3}

  • MHB
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In summary, the conversation discusses the use of rationalizing the numerator when dealing with fractions with square roots in the denominator. While it may not always be necessary, it can make adding and subtracting fractions easier. It is important to know how to do it both ways.
  • #1
xyz_1965
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I know that cot (60°) = 1/tan (60°) = 1/sqrt{3}.

Why can't we just leave it as it is? I guess my question is more about algebra than trig.

Yes, my algebra 2 days are far behind. However, back in my algebra 2 days, I never quite understood why math teachers have a problem with square roots in the denominator of a fraction.

What's so bad about a (number)/sqrt{number}?
 
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  • #2
It's not the worst thing in the world but it is easier to add or subtract fractions with integer denominators.

However, there are times when it is a good idea to rationalize the numerator. It is a good idea to know how to do it either way!
 
  • #3
Country Boy said:
It's not the worst thing in the world but it is easier to add or subtract fractions with integer denominators.

However, there are times when it is a good idea to rationalize the numerator. It is a good idea to know how to do it either way!
Understood. Thanks.
 

1. What does the equation cot(60°) = 1/tan(60°) = 1/sqrt{3} mean?

The equation cot(60°) = 1/tan(60°) = 1/sqrt{3} is a mathematical identity that shows the relationship between the cotangent, tangent, and square root of 3 for an angle of 60 degrees. It means that the cotangent of 60 degrees is equal to the reciprocal of the tangent of 60 degrees, which is also equal to 1 divided by the square root of 3.

2. Why is cot(60°) equal to 1/tan(60°) and 1/sqrt{3}?

This is due to the relationship between the cotangent and tangent functions. The cotangent is the reciprocal of the tangent, meaning that when multiplied together, they equal 1. Additionally, the tangent of 60 degrees is equal to the square root of 3. Therefore, when we take the reciprocal of the tangent, we get 1/sqrt{3}.

3. How is cot(60°) = 1/tan(60°) = 1/sqrt{3} useful in mathematics?

This identity is useful in solving trigonometric equations and simplifying expressions involving cotangent and tangent. It can also be used in geometry to find missing angles or side lengths in right triangles.

4. Can this equation be applied to angles other than 60 degrees?

Yes, this identity can be applied to any angle that has a tangent of sqrt{3}. This includes angles such as 30 degrees, 150 degrees, and 210 degrees.

5. How can I use this equation in real-world applications?

The cotangent and tangent functions are commonly used in fields such as physics, engineering, and surveying to calculate angles and distances. This identity can be used to simplify calculations and solve problems involving these functions.

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