I think your first paragraph suggests the utility of knowing some properties of 30/60/90 triangles. You learn to derive the sine and cosine values of pi/4, pi/2, pi, and 2pi in high school algebra. It doesn’t take any more memorization than knowing what the damn functions look like.
If you are seriously suggesting that supplying these values is too much trouble for you but are happy to prove general cases, then all I can say is that you must be great fun at parties.
But we still have a full day of ranting in October left! You guys are pissing me off! :mad:
Don’t look at me. I’ve been ‘detained’ since this morning. :eek:
I take back my pissedness - I didn’t realize that YOU didn’t realize there were 31 days in October. 
Thanks. Although it depends on what you mean by ‘realize.’ Consciousness and memory are such tenuous things. If only I’d understood that when I got to the the line that went “Thirty days has Octvember.” :smack: 
Sure, here New Answer - Magoosh GRE
Obviously the left side is length 1, given basic trig functions, this becomes trivial: sin(30)=1/h, thus h=1/sin(30). (Solving for the other side with tan or the Pythagorean theorem is helpful too for calculating the total distance). Then you use the property of a square having equal sides, set up a right triangle on the right side, and use more trig functions to solve the further distances that let you get the answer by simple addition.
If I can explain a perfectly valid way to solve your problem in under 30 seconds and the only thing blocking me is knowing the specific values for a specific case, your problem is not testing much that’s interesting. Especially not when it evaluates my skill to be exactly the same as someone who doesn’t know fucking triangles how do they work.
There are other issues that have largely to do with the time limit. There are many times where I can derive forms from a more general case, or come up with a formula from more basic principles without any effort, but the fact that you only have a minute and a half per problem (roughly) means that without having the specific case memorized, you’ll start falling behind because of the time you’re doing algebra. Not much, usually, but 30 seconds or a minute here and there (depending on the problem complexity) adds up. Despite the fact that you instantly know how to solve the problem, but take maybe 30 seconds to do some algebra or (rarely) basic calc, what’s apparently “better” is knowing by rote a specific form for a specific case. It’s not measuring your ability to solve the problem. It’s not even measuring your ability to solve a problem quickly (I already know exactly how to get the answer), it’s measuring your ability to recall a particular form for a particular edge case.
Okay, what is the purpose of deriving cos, sin, and tan values for those specific angles? I’ve been doing graphics and computational geometry for a while, and the number of times being able to derive them on the fly would be useful has come up never. Knowing soh-cah-toa is useful, hardcoding specific values in your brain less so. What’s useful is noting that 45deg is the midpoint where x=y, and thus at 60deg y>x and 30 deg x>y, knowing the exact values is silly. There’s nothing wrong with expressing an answer in terms of a trig function.
So yes, I will say that “providing specific values are too much trouble, but I’m happy to prove the general case”. There are times specific edge cases really matter in a qualitative way. For instance, if you’re solving the longest path problem there are algorithms that work very well and relatively quickly for directed acyclic graphs, when generalized solutions are intractable due to the nature of the problem. Knowing the exact sides of triangles with given angles off the top of your head is not a very interesting edge case.
I mean sure, you can get absurd with my argument – why know anything about right triangles when you can do it with the law of cosines? Why know the areas of anything when you can learn integration under a curve? Why know the formula for a parabola when it’s a special case of the polynomial equation Ax^2+By^2+Cx+Dy+E = 0 where either B=0 or A=0 (but not both), and the coefficient for the non-squared term for the other variable is non-zero? Hell, you can derive everything from a few axioms, make us do that! Still, knowing the specific values doesn’t test anything other than my ability to know specific values, which is a cute trick like knowing pi to 500 places, but doesn’t have many practical applications to problem solving. Especially not in fields where the general case is legitimately the important one most of the time. I’ve known computational geometry professors (including one with a world-fastest algorithm in a certain problem) that say they look up trig identities and the like when they need them.
I don’t want to act like it’s the end of the world or that I’m unable to do it, at the worst I can derive them from an equilateral triangle (just like I can derive a 45/45/90 from a square). I’m sure I’ll do relatively fine, but I maintain that it’s a silly and meaningless measure at best. I’m sure many humanities people feel similarly about the verbal.
I thought ‘no’ meant ‘yes’?
My kitchen spider died. She was keeping the fruit fly problem under control, but now she is no more. I guess the kitchen will have to smell like vinegar until her egg sac hatches.
Don’t pet stores sell tarantulas?
Tarantulas are hideous, hairy monsters made of creepy. My kitchen spider is a nice, dignified cellar spider.
I just checked and the good news is she’s not dead! 
She is, however, laying eggs so she’ll be dead soon. 
I got like two words in ten here.
I understand the words, but they don’t make no damned sense.
Two local geniuses thought it would be just a hilarious Halloween trick to pretend to attack people with a fake ax. One of the victims was a young mother with her two children. They had stopped at a gas station to change a flat tire when these morons came out of nowhere and pretended to assault her. She screamed for her kids to run and don’t stop. The two stopped, started laughing and ran off. The cops found them and they’re in jail on assault charges. Meanwhile the woman can’t sleep at night and is obviously (from an interview) still traumatized from what she thought was a life-threatening event. Fucking knuckleheads.
I guess I don’t really care so not a rant but I just saw a promo for The Following saying it would be back in January. I dropped out early to mid first season last year I think and was happy to forget about it. I guess I knew it was popular but was still surprised to see it coming back. I don’t know how Fox can produce something like this as well as Justified. I get that one is Fox and one is FX, but still. IDK. It’s not like I’ve looked at more than a few shows but it seems like Fox could do a little better and still keep their ratings.
I always lose the costume contest to a damn mermaid.
Why they are considered sexy is beyond me. Top half, great. But if ya wanna do the nasty, you end up fucking a fish. And scales, scales, scales rubbing in your netherlands. Yeah, I’ll fuck a demon chick over that any day.
I guess someone forgot that AutoCAD exists. Back when blueprints were hand-drawn, those were angles any draftsman, engineer or architect could factor in without even thinking about it (heck, I managed to “invent” Cavalier Projection before ever getting near an inkwell and I figured out the factors without knowing anything about sines or cosines). And those of us who learned geometry without calculators or tables were expected to memorize exactly those angles: they were the ones used constantly.
Well, if you look closely at this mermaid, her fishy bits don’t start until after her knees. So it’s possible, I s’pose.
I’m afraid I’m about to sound like a pretentious nerd but …
I might agree with a more general point, but I’m calling bullshit on the idea that the 30/60/90 triangle is “hard to memorize.”
Have you memorized that the sides of a 60/60/60 triangle are equal? 
What happens to a side when you bisect it? 
See? It’s just not hard to understand that sin(30°) = 0.5. Pythagoras will then give you the cosine.
When I was in college, my apartment had a kitchen spider and a bedroom spider. They were actually rather nice to have around, and they weren’t especially scary since they stayed in their webs.
I do have a big problem with closet spiders though. I opened the linen closet this morning, and found a jumping spider hanging out on the inside of the door. What the hell, spider!?!?
