Math god needed for a trig problem I concted

  • Thread starter Thread starter letsmakelotso
  • Start date Start date
  • Tags Tags
    Trig
letsmakelotso
Messages
1
Reaction score
0
hw

Delete this, please. I'm stoopid.
 
Last edited:
Physics news on Phys.org
That's not particularly special: cos of something is a number between 0 and 1, so you're taking sin of something small (less than 1 degree). So things obviously converge very quickly.
 
Do a search for small angle approximation
 
The above posters hit the nail on the head. In fact, sin(cos(tan(sin(cos(tan(sin(cos(tan(n), is not equal for any integer n. The difference is just so small that your calculator can not display the difference. Thus, the small angle approximation.

Try entering sin(cos(tan(sin(cos(tan(1) and sin(cos(tan(sin(cos(tan(1E10). If your calculator is capable of displaying enough digits, you will find that the approximate value of the first is .017452406437037, while the approximate value of the second is .017452406437039.

If your calculator can't display that many digits, use sin(cos(tan(n) instead.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

How to Determine Correct Inverse Trig Angle?
Replies
2
Views
903
Using Euler's formula to prove trig identities using "sum to product" technique
Replies
4
Views
2K
Calculus 2 - Trig Integrals Question (Integrating cos^2x)
Replies
3
Views
2K
Trig Substitution Problem w/ tan substitution
Replies
4
Views
1K
Calc BC derivative problem with trig and double angle -- Help please
Replies
1
Views
1K
I Practice With Proofs? (Algebra, Trig, and Calc)
Replies
6
Views
2K
Help with this Integration please
Replies
4
Views
1K
How Do You Solve the Integral ∫x/(6x-x^2)^3/2 dx Using Trig Substitution?
Replies
2
Views
1K
Fourier Transform - Solutions Error?
Replies
5
Views
1K
Evaluating Limits with trig functions
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top