<p>do you guys remember abou the question where it asked which of the following equals to 1 for all values of x</p>
<p>I. sinx cscx
II. 2sinx cosx
III. sin^2 x + cos^2 x</p>
<p>was the answer I and III, or only III?</p>
<p>Wait a second. For the number of imaginary roots problem, I factored the cubic and got
(x - 1)*(2x + 1)^2</p>
<p>Does anyone remember the original polynomial?</p>
<p>@csc2400
The answer was both I and III because sinx*cscx = sinx/sinx and sinx != 0 on (0, pi/2).</p>
<p>how about when x=0 for sinx cscx</p>
<p>the interval given didn’t include 0, so it doesn’t matter.</p>
<p>asdf: The original polynomial was 4x^3 - 3x^2 - 1. If you plug it into Wolfram Alpha, it shows there’s only one real solution, and the graph only intersects the x-axis once.</p>
<p>Clarinet: sin x csc x isn’t the same as 1, because whereas when you have f(x) = 1, you can say f(0) = 1, in sin x csc x, x = 0 is not defined. It’s the same reason why in something like (x^2-4)/(x-2), x = 2 is not defined (there’s a hole in the graph) but when solving for the limit you can cancel out. However, in this problem it didn’t matter because the interval didn’t include 0.</p>
<p>sinx*cscx isn’t equal to one. It is actually a function, it just happens that cscx evens out the sinx so that it’s equal to 1 everywhere except when x = 0.</p>
<p>do you guys remember any other questions?
i want to know if i made any more mistakes…</p>
<p>After taking the test guys, any areas you recommend studying a lot? And any review books to get?</p>
<p>The only study guide I used was Barron’s, but few questions on the test were actually relevant to the study guide. I would go with the official one.</p>
<p>It was just III, which I think was sqrt(sin^2(x) + cos^2(x)).</p>
<p>"It was just III, which I think was sqrt(sin^2(x) + cos^2(x)). "</p>
<p>Why not I? sin(x)csc(x)</p>
<p>No, it was both I and III.</p>
<p>^^ That is what I put. :D</p>
<p>sqrt(sin^2(x) + cos^2(x)) is always equal to one regardless of what x is.
sin(x)*csc(x) isn’t always equal to one because there’s a hole where x = 0.</p>
<p>SEMAPHORE THE DOMAIN WAS RESTRICTED GODDAMMIT
let’s move on now.</p>
<p>Who’s looking forward to February 16th :D</p>
<p>Oh, gosh, I know I am.</p>
<p>Me too. :D</p>
<p>What do you guys expect the curve to be? What raw score for an 800?</p>
<p>Exactly. Since x is restricted to x > 0, x = 0 is NOT included.</p>