Given spherical and cylindarical coordinates, draw each one

sinned4789
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Homework Statement


part 1) draw 3(R-hat) + 3(theta-hat) + 3(phi-hat)
part 2) draw 3(r-hat) + 3(theta-hat) + 3(z-hat)


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The Attempt at a Solution


aren't these the same thing? just 3 in each of the x, y, and z directions in cartesian coordinates.
 
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Absolutely not. Look up the wiki pages on spherical and cylindrical coordinates.
 

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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