# Tagged Questions

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### Exact calulation of trigonometric functions

My question is a bit related to computer science and I am not quit sure if this place is a good one for it. Let me know if I should move it. So as you know values of functions like sin or cosine can ...
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### Rational approximation of $\tanh\,(\sqrt[4]{s}$)

I'd like to find a rational representation of $$f(s) = \frac{\tanh\,\sqrt[4]{s}}{\sqrt[4]{s}}= \frac{a_0 + a_1 s + a_2 s^2 + ... + a_n s^n}{b_0 + b_1 s + b_2 s^2 + ... + b_m s^m}$$ For the case ...
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### Why does $\arctan(\frac{\tan \theta}{2}) \approx \frac{1}{2 - \theta} - \frac{1}{2 + \theta}$ for small $\theta$?

In answering this question, I needed to show that $\arctan \left( \frac{\tan \theta}{2} \right) \approx \frac{\theta}{2}$ when $\theta$ was small. So, naturally, I computed the first few terms of the ...
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### Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$

Just curious, is there a geometry picture explanation to show that $\sqrt 2 + \sqrt 3$ is close to $\pi$?
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### Approximation to $\sqrt{\cos(\theta)}$?

I have this formula, (it is just the law of cosines angle formula): $$d = \sqrt{a^2 + b^2 - 2ab \ cos(\theta)}$$ Here is my issue. I am wondering if there is a way to 'extract' the $cos$ term. My ...
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### Approximating Trig Functions with Polynomials

I was thinking about the graphs of different trig functions and noticed that most of them are of a similar shape to some different types of polynomials. For example: Higher degree polynomials create ...
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### $\sin x$ approximates $x$ for small angles

In physics, particularly in waves, we make use of the fact that for small angles (less than $\pi/12$-ish), the sine function value of an angle is pretty close to the value of the angle itself (in ...
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### Numerical Approximation Involving Trig

I have a graphics problem that reduces to this: (Computer equation) alpha = arctan(X / ((Y / (Z * cos(alpha) - k)) * Z * cos(alpha))) (LaTeX) \alpha = ...
Let $\theta_{kl}$ be an angle such that $\cos\theta_{kl}=\frac{1}{2}(\cos(\frac{2\pi k}{n})+\cos(\frac{2\pi l}{n}))$. Given that definition, if I introduce a new variable $t$ is the following a ...