Evaluate trig functions at infinity?

AStaunton
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is it meaningful to evaluate cos and sin at infinity? I ask in relation to Fourier integrals...

ie does cos(infinity) have a value
 
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The improper integral of sin(x) or cos(x) from zero to inf does not converge or diverge
so you can't evaluate it.
 
AStaunton said:
ie does cos(infinity) have a value

You tell me. What does the graph of cosine look like? Is cos(x) going to approach a certain number as x approaches infinity?
 

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...
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