MHB Cot (60°) = 1/tan (60°) = 1/sqrt{3}

  • Thread starter Thread starter xyz_1965
  • Start date Start date
Click For Summary
Cotangent of 60° equals 1/tan(60°), which simplifies to 1/sqrt{3}. The discussion centers on the preference for avoiding square roots in the denominator of fractions, as it can complicate addition or subtraction of fractions. While having a square root in the denominator isn't inherently problematic, rationalizing it can simplify calculations. Understanding both methods is beneficial for mathematical proficiency. Ultimately, the conversation highlights the balance between mathematical conventions and practical ease in calculations.
xyz_1965
Messages
73
Reaction score
0
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}?
 
Mathematics news on Phys.org
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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB Solving $\tan^2x + \tan^2{2x} + \cot^2{3x} = 1$ in R
  • · Replies 6 ·
Replies
6
Views
1K
MHB Prove (tan^2 t−1)/(sec^2 t)=(tan t−cot t)/(tan t+cot t)
  • · Replies 3 ·
Replies
3
Views
2K
Why Is My Argument Calculation for Complex Number Incorrect?
  • · Replies 14 ·
Replies
14
Views
2K
MHB Evaluate Trig Expressions....Part 1
  • · Replies 2 ·
Replies
2
Views
2K
MHB Sum of Infinite Series: cot^-1(5/sqrt(3))+cot^-1(9/sqrt(3))+...
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
  • · Replies 16 ·
Replies
16
Views
992
MHB Express cos(2 tan^-1(x/4)) and sin(2tan^-1(x/4) as an algebraic expression in x
  • · Replies 3 ·
Replies
3
Views
2K
MHB Challenge: Is cos(pi/60) transcendental?
  • · Replies 1 ·
Replies
1
Views
2K
High School Expressions of ##log(a+b), tan^{-1}(a+b),sin^{-1}(a+b)##,etc
  • · Replies 12 ·
Replies
12
Views
2K
How Does Adding π/2 Affect the Sign of Tan and Cot in Trigonometry?
  • · Replies 5 ·
Replies
5
Views
2K