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Ultimate Math Sheet

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    I LOVE YOU Oh and, not sure, but, aren't you missing the: 1/2absinC? (calculates area of a triangle when you have two lengths and an angle in between)
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    Are you missing graph theory? Also where is logarithms
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    > **Posted by Godsmack** > Are you missing graph theory? > Also where is logarithms I have not learned logarithms or graph theory yet. This math sheet is so I won't forget the math I've learned. I made this math sheet because one time, I was doing some math that involved long division and then I realized that I was doing long division wrong >_>, it was embarrassing when I had to ask the college math tutors about long division..... so I made this giant sheet so I can always have quick review material.
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    How old are you dude, this shit is like the lowest basis of mathematics? Also, you're missing quite a lot.
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    > **Posted by agent** > How old are you dude, this shit is like the lowest basis of mathematics? Also, you're missing quite a lot. 21, just saved up enough money to go to community college. how about u don't complain about what's missing and gimme some formulas and their explanations to add to the sheet? :)
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    I forgot to mention that i'll be adding formulas from what I learn in AP Physics.
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    > **Posted by Kevinsk** > > 21, just saved up enough money to go to community college. > > how about u don't complain about what's missing and gimme some formulas and their explanations to add to the sheet? :) Sorry if I came off as a dick in my previous post. Generally speaking, memorizing a bunch of formulas and mathematical identities is a bad way to learn math, especially if you want to use it more than to just pass your exam. It's much better to actually understand concepts behind those formulas. And the phrase "there is more than one way to skin a cat" is also true for mathematics, and at least for me, that's the best part about mathematics. Let me illustrate this concept with a rather simple example. Let's prove the fundamental identity of trigonometry, _sin²(x) + cos²(x) = 1_. Let _ABC_ be triangle with angles _alpha_, _beta_ and _gamma_. Let's assume that _gamma_ is a right angle (pi/2, 90 degrees). Let _c_ be hypotenuse, and _a_ and _b_ catheti. Now we know that _sin(alpha) = a / c_, and _cos(alpha) = b / c_. Take both of these equations, square them and then add them together. What we have now is this: _sin²(alpha) + cos²(alpha) = (a² + b²) / c²_. From Pythagorean theorem, we have that _a² + b² = c²_, which simplifies our equation to _sin²(alpha) + cos²(alpha) = c² / c²_. As _c² / c² = 1_, it concludes proof that _sin²(alpha) + cos²(alpha) = 1_. Well that was interesting, but it isn't the only way to prove this identity (well, strictly mathematically speaking, this proof is rather 'bad' because it has too many assumptions, but don't bother yourself with that). For example, here is another proof of the same identity using derivatives of functions _sin(x)_ and _cos(x)_. It's proven that _(sin(x))' = cos(x)_ and _(cos(x))' = -sin(x)_. Let _f(x) = sin²(x) + cos²(x)_, then derivative of _f(x)_ is _f'(x) = 2sin(x)cos(x) + 2cos(x)(-sin(x)) = 2sin(x)cos(x) - 2cos(x)sin(x) = 0_. So, the first derivative of _f(x)_ is 0, that means _f(x)_ is a constant value function (_f(x)_ takes the same value in every point of its domain), let's call this value _t_, so _f(x) = t_. If _f(x)_ equals _t_ in every point of its domain, it must equal _t_ in 0. So, _f(0) = t, f(0) = sin(0) + cos(0) = 0 + 1 = 1_, and from there, _t = 1_. Well this kinda got a bit long, but I hope I succeeded to interest you a little bit more into the world of mathematics.
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    > **Posted by agent** > > **Posted by Kevinsk** > > > > 21, just saved up enough money to go to community college. > > > > how about u don't complain about what's missing and gimme some formulas and their explanations to add to the sheet? :) > > Sorry if I came off as a dick in my previous post. Generally speaking, memorizing a bunch of formulas and mathematical identities is a bad way to learn math, especially if you want to use it more than to just pass your exam. It's much better to actually understand concepts behind those formulas. And the phrase "there is more than one way to skin a cat" is also true for mathematics, and at least for me, that's the best part about mathematics. > > Let me illustrate this concept with a rather simple example. Let's prove the fundamental identity of trigonometry, _sin²(x) + cos²(x) = 1_. > > Let _ABC_ be triangle with angles _alpha_, _beta_ and _gamma_. Let's assume that _gamma_ is a right angle (pi/2, 90 degrees). Let _c_ be hypotenuse, and _a_ and _b_ catheti. Now we know that _sin(alpha) = a / c_, and _cos(alpha) = b / c_. Take both of these equations, square them and then add them together. What we have now is this: _sin²(alpha) + cos²(alpha) = (a² + b²) / c²_. From Pythagorean theorem, we have that _a² + b² = c²_, which simplifies our equation to _sin²(alpha) + cos²(alpha) = c² / c²_. As _c² / c² = 1_, it concludes proof that _sin²(alpha) + cos²(alpha) = 1_. > > Well that was interesting, but it isn't the only way to prove this identity (well, strictly mathematically speaking, this proof is rather 'bad' because it has too many assumptions, but don't bother yourself with that). For example, here is another proof of the same identity using derivatives of functions _sin(x)_ and _cos(x)_. > > It's proven that _(sin(x))' = cos(x)_ and _(cos(x))' = -sin(x)_. Let _f(x) = sin²(x) + cos²(x)_, then derivative of _f(x)_ is _f'(x) = 2sin(x)cos(x) + 2cos(x)(-sin(x)) = 2sin(x)cos(x) - 2cos(x)sin(x) = 0_. So, the first derivative of _f(x)_ is 0, that means _f(x)_ is a constant value function (_f(x)_ takes the same value in every point of its domain), let's call this value _t_, so _f(x) = t_. If _f(x)_ equals _t_ in every point of its domain, it must equal _t_ in 0. So, _f(0) = t, f(0) = sin(0) + cos(0) = 0 + 1 = 1_, and from there, _t = 1_. > > Well this kinda got a bit long, but I hope I succeeded to interest you a little bit more into the world of mathematics. Yea but I can't learn math without memorizing the formulas and properties. It's just how I learned it... This is especially the case with geometry and it's multitudes of formulas for shapes. By making this quick review sheet, I can make sure I never forget. Besides, all this trig, geometry, and graphing mathemas is useful for mapping as well as modelling.
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    I finished Geometry and lumped all Triangles into 1 big block with their respective Areas and Perimeter.
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