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There's a pre-calculus test tomorrow and I'm lost
I already asked the homework help thread at TVTropes, but I have a feeling that asking around isn't going to prepare me nearly enough. I might very well be screwed on the test. I also think it's pathetic of me to be lost on something that's merely preparation for calculus.
Why does it have to be the first class of the day? I'm barely awake at that time. Not to mention the teacher has swarmed us with practice problems, many of which seem completely unrelated. >_>
Comments
Ugh, Calculus. :P Are you having trouble with anything in particular?
Edit: Ninja'd
recall:
You can substitute sin(x) = a, cos(x) = b, and tan(x) = c as if they were regular variables and then it's just algebra
tan(x) = sin(x)/cos(x)
x^2 - y^2 = (x + y)(x - y)
It's all memorization and strategy.
For the record 1=cos2(x)+sin2(x)
^^Focus on the problems that you think you can get and leave the others until you're done with the "easy" problems. Then take the test to your tutor when you get it back. That should help.
Sometimes you have to have a bad semester and retake something and then you get caught back up because you start to understand the material again.
...that's just bull. Gimme a moment to work out a sequence of mathematical steps that will follow that bull of a rule and still prove it.
^correct.
It's not that bad though
(sin(x) + cos(x)) / (1 - tan^2(x)) =
(sin(x) + cos(x)) / (1 - sin^2(x) / cos^2(x)) =
(sin(x) + cos(x)) / (cos^2(x) / cos^2(x) - sin^2(x) / cos^2(x)) =
(sin(x) + cos(x)) / ((cos^2(x) - sin^2(x)) / cos^2(x)) =
((sin(x) + cos(x)) * cos^2(x)) / (((cos^2(x) - sin^2(x)) / cos^2(x)) * cos^2(x)) =
((sin(x) + cos(x)) * cos^2(x)) / ((cos^2(x) - sin^2(x)) =
((sin(x) + cos(x)) * cos^2(x)) / ((cos(x) + sin(x))(cos(x) - sin(x))) =
(((sin(x) + cos(x)) / ((sin(x) + cos(x))) * cos^2(x)) / (((cos(x) + sin(x))(cos(x) - sin(x))) / ((sin(x) + cos(x))) =
cos^2(x) / (cos(x) - sin(x))
Now if you HAVE to do it with one side only:
[ (sin x + cos x) / (1 - tan^2 x) ] * [ (cos x - sin x) / (cos x - sin x) ]
= (cos^2 x - sin^2 x) / [ (1 - tan^2 x) (cos x - sin x) ]
= (cos^2 x - sin^2 x) / [ (1 - sin^2 x / cos^2 x) (cos x - sin x) ]
= (cos^2 x - sin^2 x) / { [ (cos^2 x - sin^2 x) / (cos^2 x) ] (cos x - sin x) }
= 1 / [ (1 / cos^2 x) (cos x - sin x) ]
= cos^2 x / (cos x - sin x)
^ ehh it's okay, lol
(sin^2(y)+sin(y)cos(y)+cos^2(y))(sin(y)cos(y))/(sin(y)-cos(y))=
(1+sin(y)cos(y))(sin(y)cos(y))/(sin(y)-cos(y))=
1+sin(y)cos(y)=sin(y)cos(y)+1
^^ Physics is pretty heavily based on calculus. And engineering is pretty heavily based on physics. So that's at least one thing. That said, learning math for the sake of being able to do math is also a good idea. Frankly, there's absolutely nothing they teach you in school that is useful in every single possible career a person might have. That doesn't mean it isn't valuable.
That skill--general problem-solving--is a skill whose usefulness spans everything from business management to industrial engineering to policy design to writing research papers for class.
Calculus is also good for:
Differentiation: if you know the equation, you can find the slope at any point. Useful for engineering, finance, etc.
Integration: if you know the equations for the perimeter, you can find the area. Useful for surveying, engineering, planetary physics, aerospace, etc.
Integration: Useful for knowing that many, many little pieces can add up to something really freakin' huge.