Cot (60°) = 1/tan (60°) = 1/sqrt{3}

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SUMMARY

The discussion centers on the mathematical identity cot(60°) = 1/tan(60°) = 1/sqrt{3} and the rationale behind rationalizing denominators in algebra. Participants express that while having square roots in the denominator is not inherently problematic, it complicates operations like addition and subtraction of fractions. The consensus is that understanding both forms is essential for mathematical proficiency, particularly in algebra.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cotangent and tangent.
  • Familiarity with algebraic concepts, particularly rationalizing denominators.
  • Knowledge of square roots and their properties.
  • Basic skills in fraction addition and subtraction.
NEXT STEPS
  • Study the process of rationalizing denominators in algebra.
  • Explore the properties of trigonometric functions and their identities.
  • Learn about the implications of square roots in mathematical expressions.
  • Practice addition and subtraction of fractions with both rational and irrational denominators.
USEFUL FOR

Students revisiting algebra concepts, educators teaching trigonometry and algebra, and anyone looking to enhance their mathematical understanding of rationalizing expressions.

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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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!
 
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.
 

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