<p>Solve the equation sin15x + cos15x = 0. What is the sum of the 3 smallest positive solutions?</p>
<p>(A) pi/20</p>
<p>(B) pi/3</p>
<p>(C) 7pi / 20</p>
<p>(D) 21pi / 20</p>
<p>(E) 21pi / 4</p>
<p>I skipped it on a practice test, because I didn’t have time to do it by hand… is there some efficient way to solve this on an 89?</p>
<p>(Answer is C)</p>
<p>There is…I did it last semester in school but I really don’t remember, I’ll try looking at it</p>
<p>I suggest doing some of the division in your head and then plugging in each of the answers, starting with C, the middle answer. From there you can determine whether the answer should be higher or lower and could eliminate 2 more answers. Since 15/20 = 3/4, you just plug in sin(7/4pi)+cos(7/4pi) = 0. It shouldn’t take more than a minute to do this, which should put you on par for the test.</p>
<p>well you know that sin15x=-cos15x. This occurs when 15x=(3/4)pi + n(pi)…where n is an integer. So divide both sides by 15 and you get:
x=(3/60)pi + (n/15)pi or x=(1/20)pi +(n/15)pi. The three smallest terms would occur when n equals 0,1, and 2. So the values are (1/20), (1/20) + (1/15), and (1/20) + (2/15). Adding all of these values up gives you 7pi/20. It’s not a long problem at all…it only took me about 30 seconds.</p>
<p>graphing it on ur calc is probably the easiest way</p>
<p>y=sin(15x)+cos(15x)</p>
<p>graph and find sum of 3 smallest zeroes</p>
<p>Or graph sin15x and -cos15x and find sum of the x-values of the three first times they intersect. Either way works.</p>
<p>Oh, ok. Thanks guys :)</p>