Formulas Definition and 522 Threads

sin(a + b) = sin(a)cos(b) + cos(a)sin(b) sin(a - b) = sin(a)cos(b) - cos(a)sin(b) cos(a + b) = cos(a)cos(b) - sin(a)sin(b) cos(a - b) = cos(a)cos(b) + sin(a)sin(b) Who first derived them? When, and how? Thanks

Hello. I know the definition of sine and cosine, but how were these formulas originally invented? I mean, how did people derive the power series for sine and cosine for the first time?

Does ne1 know of any free math programs that write formulas and make graphs? I need one for a project I'm working on.

Homework Statement does anyone know how i can differentiate a strong acid from a weak acid and likewise for a strong base and a weak base based on its chemical formula? Homework Equations The Attempt at a Solution

Homework Statement What is the formula for: Fn, Ff, and mu when you have a object sliding down a ramp. Variable know are D, T, A, Vi, and the angle of the ramp above the horrizon. The Attempt at a Solution I've tried a few that ended up being quite long and all wrong...

Presenting the aberration of light effect we consider that two observers at rest in I and I' in the standard configuration equipped with laser guns start to emit light when they are instantly located at the same point in space. The problem is to find out a relationsship between the directions...

Homework Statement First of all this is revision not homework =) question is Xn+1 = Cuberoot ( 17.5-2xn) answer lies between 2 and 3. i know the answer is 2.34 but what i don't get is why it is xn+1 = equation, because when you put xn=2.34 into the equation you get 2.34 out...

Homework Statement What is the acceleration,position,and velocity formula for the launch of a slingshot. Homework Equations The Attempt at a Solution I just don't know where to start tbh... I really need help i put this off and its due tommorrow... If someone could respond i can...

Derive formula #5 using any of the other formulas 1. Vav= d/t 2. Aav= V2-V2/t 3. d= (V1+V2/2) t 4. d= V1t + 1/2 a t squared 5. V2 squared = V1 squared + 2ad *note all the Vav, Aav, a and d have a vector sign ontop and d and t always have the triangle representing change in

1. My teacher has given me a poster board to do on magnetic energy even though she has explained nothing about the subject, nor is there anything in my book. I am looking for the formula for finding magnetic energy and examples from everyday life. All I got was 1/2BH, but I have no idea what...

I am interesting for mathematical background od fast algorithms for computing number \pi with complete proofs only. More specific, I am interesting for Gauss Legendre algorithm, Borwein algorithm, Ramanujan formulas and Chudnovsky formula.

Homework Statement The given equation is: 0 = vt-1/2at^2 and you must solve for t.Homework Equations There's a question similar to this one, d=ut+1/2at^2, but there's an extra variable so you are able to use the quadratic formula. In this case, I'm not quite sure if I'm solving the question...

Hello all. I'm investigating a little bit about stokes law in order to understand the settling velocity of falling particles and on the net i encountered with 2 different formulas and i simply can't find the reason why they are different. every formula gives me a different answer. The 2...

I'm looking for a giant tome on every theorem and formula. If it had more, that would be awesome, but I'm just looking for one giant book to use as a reference. I prefer to learn theorems and formulas after learning how they were discovered, but I also want a "scope" of what's available out...

Part 1:Factor the expressions a^2-b^2 and a^3-b^3 For part 1, i worked it out to be: (a+b)(a-b) and (a-b)(a^2+ab+b^2) Part 2: Suppose f(x) is a function that has a derivative. Let g(x)=x^2f(x), k(x)=\sqrt{f(x)}, and p(x)=^3\sqrt{f(x)}. Without using the product rule and w/o using the...

I am writing a science fiction book with the following premise: A starship drive (and weapon) has been discovered that acts as a laser that turns ordinary matter into gamma rays at 100% efficiency; matter goes in one end of a tube and the light comes out the other end, driving the spaceship...

Homework Statement Prove that sin (a+b) does not equal sin a + sin b. Let a = pi/3 and b = pi/6 Homework Equations The Attempt at a Solution Where I am lost is how to figure out what pi/3 or pi/6 is. Like for example, how can I know sin pi/3 is sqrt3 over 2? Is this a...

Homework Statement Taking e to be small, we have been given these two formulas to prove m1 = \frac{-1+\sqrt{1-4e}}{2e} = \frac{-1+(1-2e+O(e^2))}{2e} = -1+ O(e) m2= \frac{-1-\sqrt{1-4e}}{2e} = \frac{-1-(1-2e+O(e^2))}{2e} = -1+ O(1) Homework Equations The Attempt at a Solution...

I have a test coming up tomorrow, looking for all the equations, I am in AP Physics course. TY

Homework Statement Identify the group to which X belongs in each ionic compound formula. Enter your response using the group number. a) MgX b)XCl2 c) XF2 Homework Equations The Attempt at a Solution The first one I figured out was group 16. However, the next two I thought...

as the topic, just want ask what software does that sort of things. thanks

Homework Statement sin^3(x) - cos^3(x) / sin(x) + cos(x) = csc^2(x) -cot(x) - 2cos^2(x) / 1 - cot^2(x) Homework Equations The Attempt at a Solution I have attached one of my many attempts. Any input?

Homework Statement I'm given the values: UH=2031, BH=36927 and VH=146405 and I'm asked to solve the following equations iteratively to find UJ BJ and VJ. Homework Equations UJ=UH+0.179(BJ-VJ) BJ=BH+0.060(BJ-VJ) VJ=VH-0.004(BJ-VJ) I don't know how to solve equations iteratively...

"Normal form" for formulas I am about to set myself the following programming exercise; let me know if this would be useful in any way, or how can it be improved into something useful. Suppose I restrict myself to formulas in polynomials of Q, including polynomial fractions. My intention is...

I'm a student that isn't quite understanding how to write formulas for compounds. any help would be appreciated. thanks.

First, Is there a way to convert a complex number to polar form without using boolean commands? And now, my real question: Do all of viete's formulas hold true when the coefficients of a cubic formula are complex? I wrote a script that finds the roots of a cubic formula with complex...

Homework Statement Determine which of the formulas hold for all invertible nxn matrices A and B: (a) (A+A-1)8=A8+A-8 (b) A + In in invertible (c) AB=BA (d) (A+B)(A-B) = A2 - B2 (e) (ABA-1)3 = AB3A-1 (f) A6B4 in invertible The Attempt at a Solution (a) I don't know this one, I don't...

zE=kE=mv² / 2, pE=brE=mgh, F=GMm/r²=Erk, F=kp1 q2/d², fx=mv²/2 Could you proof the formulas above?and also Galileo's h=gt²/2 Can you proof them?

Suppose we have a number of formulas involving variables a,b,c,d,e,f. What does it mean when the text says let M(a,b,c,d,e,f) be the conjunction of the formulas?

About these formulas: \frac{n(n+1)}{2}, \frac{n(n+1)(2n+1)}{6} ,(\frac{n(n+1)}{2})^2 How were they evolved? And what about i^4, i^5, i^6,... Thankyou everybody;;

I am in a Chem 105 course. I don't have a homework assignment but we do have a test coming up and I have some worksheets to help me practice writing formulas. My question is how do you know if the formula has a charge. For example: Sodium Nitrate - I know Sodium is Na and I know Nitrate is a...

hello. i need help deriving trig formulas. the first problem i most derive is 51. sin^2 x + cos^2 x = 1 i can use these identities: a. sin(-x) = -sinx b. cos(-x) = cos(x) c. cos(x+y) = cosxcosy - sinxsiny d. sin(x+y) = sinxcosy + cosxsiny thanks for any help

Homework Statement rearrange the formula d=Vft-1/2at^2 to solve for a Homework Equations d = Vft-1/2at^2 d+ 1/2at^2 = Vft 1/2at^2 = Vft-d 1/2a = Vft-d / t^2 then does a = 2 (Vft-d / t^2) The Attempt at a Solution

Homework Statement Write the formula for Ammonium Sulfide Homework Equations NH4^+ = ammonium S^2- = Sulfur The Attempt at a Solution NH4^+2S

many people have sent me links to answer my questions. i have read them and i do understand them. i have the ability to picture how general relativity works. however when i see mathematical formulas on these sights u send me they really mean nothing. is there a link you can send me that i can...

hey is there a formula for compression and tension? if so would you be able to let me know what they are? thanks! :)

How do you write the permutation and combination formulas using latex. This is the best I can do: n_P_r=\frac{n!}{(n-r)!}

Homework Statement Let C. denote the circle |z-z.|= R, taken counter clockwise. use the parametric representation z= z. + Re^(io) (-pi </= o </= pi) for C. to derive the following integration formulas: integral C. (dz/(z-z.)) = 2ipi Homework Equations note: z. and C. represent z knot...

using those formulas, how would you solve tan 11 pi ----- 8 and cot 195 also, how would you prove tan (x +y ) = tan x and tan ( pi/4 -x) = 1 - tan x --------- 1 + tan x thank you so much for any help

If events A and B are in the same sample space: . Proove that if P(A I B') > P(A) then P(B I A) < P(B) (where B' is the Probability of A given not B) . Proove that if P(A I B) = P(A) then P(B I A) = P(B) do we assume independence here so that P(A I B) = [P(A)*P(B)]/ P(B) = P(A)...

i have two different beam deflection formulas, one for rigid supports and one for simple supports - but i know there are many different ones out there. i was wondering if anyone could tell me how the formulas were created, oh and also what exactly does moment of inertia have to do with...

Homework Statement Evaluate: \int\int \phi \nabla(\frac{1}{R}) - \frac{1}{R}\nabla\phi * \vec{n} dS a) over the surface of the ellipsoid 1/9\,{x}^{2}+1/16\,{y}^{2}+1/25\,{z}^{2}=1 > where \phi={x}^{2}+{y}^{2}-2\,{z}^{2}+4 Homework Equations The Attempt at a...

My fluid dynamics is rather weak and i was wondering if someone could please tell me how to calculate dynamic head of the flow in the a tube and how to calculate pressure drop of a hole in a tube? Some formulas would be handy thanks engineering

Hi, I'm working on some simple aerodynamics for a game. Are there any generic, but fairly accurate, formulas for calculating the lifting force (N) required for aircrafts that use aerofoils, and another for calculating the amount of air that needs to be displaced (m^3/s) for aircrafts that in one...

Okay, the formula that I am working from is: (RL+S) – sqrt [ RL^2 – (S*sin CA)^2 ] – S*cos CA Rod Length = RL = 5.090 Half Stroke = S = 1.5 Crank Angle = CA = 107.5 With numbers plugged in (my version?): (5.090+1.5) - sqrt [5.090^2 - (1.5*sin (107.5))^2] - 1.5*cos (107.5) The...

Just curious, often in math I am presented with formulas and I always study them the day before the test; however, two weeks later, I cannot recall one formula. Am I the only one that does this? If so, I better be off and start learning them(I plan to). For instance, formulas like the finite...

[SOLVED] Work-Energy Theorem I'm sorry that I do seem to require quite a bit of help, but sometimes when the formulas just aren't working for me I get desperate. Homework Statement A force is applied to a 2.5kg- radio-controlled model car parallel to the x-axis as it moves along a...

Is there any kind of formula that exists or I can put together that will allow me to determine airflow from a fan being funneled into a tube that decreases in size over the length of the tube? Something specifically that would allow me to determine the air pressure (psi ?) coming out the end of...

I have been torturing myself with this problem for a couple weeks now and I am stumped. The unit I am working on is called simple harmonics. The question is: Prove that the maximum speed (Vmax) of a mass on a spring is given by 2(pi)fA I am guessing that the question wants me to re-arrange one...

Homework Statement A: 1 To play tennis at the local tennis club costs 150 kr/hour for non-members and 90 kr/hour for members. A membership costs 2100 kr a year. How many hous of tennis does one have to play to make it wothwhile to be a member? (kr is the swedish currency) 2 In a...