Just finished another calculus quiz - my fastest time yet! Even better, 100%. I am, however, puzzled by one of the questions.
f(x)=7 sec(x), from [-pi/4, pi/4] I had to find the first derivative to find the critical point, then use the boundaries and critical point to find absolute minimum & absolute maximum. Not too hard. I plug f and f' into the calculator, evaluate at -pi/4, 0, and pi/4, and get results of 9.899495, 7 and 9.899495.
Only problem is, I can tell from how the answer slot is labeled that they're not looking for a decimal. I found a similar problem in the book that showed the max of sec(pi/4) as √2. I tried evaluating 7√2, sure 'nuff = 9.899495.
What puzzles me is how to evaluate sec(pi/4) to get the radical of √2 as an answer. Is it something in the trigonometric identities?
Since cos(π/4) = 1/√2 (you probably remember this from trig), sec(π/4) = √2
Ha! My trig is ~12 years old. I did a lot of brushing up in the first two weeks of this course but remain weakest on trig. I'd be completely lost if Chem (last summer) and Physics (fall) hadn't started the brushing up.
I missed the part where cos(pi/4) = 1/√2.
The unit circle in my book's appendix shows that for 45 degrees = pi/4 = (√2/2, √2/2). Given this is a unit circle, cos(pi/4) is the x coordinate, yes? So then
√2/2, multiply by √2/√2 to get 2/2√2, cancel the 2's to get 1/√2? And then, since sec(x) = 1/cos(x), the secant(pi/4) is √2/1 = √2?
eta: DK - I was all set to ignore the √2 video then watched it. It wouldn't have helped, but it was actually very interesting and fun to watch. Thank you!
Your first mistake was picking up your calculator by default. Most of this stuff can and should be done on paper and/or in your head if you know what you're doing.
Agreed, which is why I'm trying to learn how to do it that way. I don't just want the right answer, I want to know I got it correctly. I'm glad you and other BGG'ers have been generous in helping when I've gotten stuck.