<p>How would you find the points of intersection of the graphs of the square root of sine of x and (x-2) squared without a calculator?</p>
<p>I couldn't think of a quick answer, so here's what I did: I squared both sides, and so we have Sin[x] = (x-2)^4. Then, I used the third-order expansion of Sin[x]. Then, solving with the quartic equation, we see that the graphs must cross at x = ~ 1.03924.</p>
<p>I know, I know, this is only computational. But, how would you do it, otherwise?</p>
<p>Use Newton's method if applicable.</p>
<p>Alright thanks I really have no idea what you're talking about with the third order expansion of sine but we got the same answer so I guess it works.</p>
<p>just curious...what subject is this question for?</p>