Sketching H(sin(x)): How to Graph a Step Function with a Sine Argument

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Homework Statement



sketching

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How to sketch H(sin(x)) if H(x) is a step function

How would you start ?!
 
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Do you have a specific step function in mind? Over what interval are you trying to graph it?

I think the simplest way would be to just divide the whole function up into n sub intervals that are the length of the step.
 
that was a question on an old exam! nothing more.

the step is assumed
H(x) = 1 if x>0
H(x) = 0 if x<0
 
scientific1 said:
that was a question on an old exam! nothing more.

the step is assumed
H(x) = 1 if x>0
H(x) = 0 if x<0

Use that definition to write what H(sin(x)) is. (Replace x by sin(x) everywhere in the definition).
 
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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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