Sin Definition and 452 Threads

this example was in a book I bought ( maths methods for physics, Mathews and Walker) dy/dx + sqrt( (1-y^2) / (1-x^2) ) = 0 dy/(1-y^2) + dx/(1-x^2) = 0 sin -1 y + sin -1 x = c [1] or, taking the sine of both sides x (1-y^2)^1/2 + y...

b2cos2θ+2cosθ(-mb+bc2-bz-bcsinθ)+2sinθ(cm-cz)-c2sin2θ=p How to get θ in terms of b,c,m,z,p The equation i formed to calculate the dynamic PLs, anyone can help to solve this, i would much appreciate! I am doing my FYP!

Homework Statement [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP120619i0ea2h15bci31300005d9a3422292h43h4?MSPStoreType=image/gif&s=43&w=174&h=39 Homework Equations The Attempt at a Solution So Wolfram says to use L'Hopital as the first step, we haven't learned anything about this...

Integral descriptive: \int _{0}^{\pi }\! \left( a+{\it k1}\,\sin \left( \theta+{\it beta1} \right) \right) {e}^{{\it k2}\,\sin \left( \theta+{\it beta2} \right) }{d\theta} I think if beta1 and beta2 come to zero,i may be a typical integral.However,in this integral,beta1 and beta2 are...

I'll be applying to grad schools in the coming months, and I'm mostly interested in programs that involve nonlinear dynamics, synchrony, and chaos. But, my undergraduate research is in two other areas, different from each other and not involving nonlinear dynamics at all. I've worked on...

Homework Statement 1) how to prove that sin square x cos square x is identical to 1/8 (1- cos 4x)? 2) f(x) = x square +7x -6 ----------------, show that when x is sufficiently small for (x-1)(x-2)(x+1) x^4 and higher powers to be neglected. Homework Equations 1) cos (s +...

When I did this problem I overlooked the fact that a u-sub of u=cos x would work fine. I ended up using the more complicated trig integrals rules and did this: ∫cos5 x sin x dx ∫(cos2 x)2 cos x sin x dx ∫(1 - sin2 x)2 cos x sin x dx ∫(sin5 x - 2 sin3 + sin x) cos x dx with u = sin x, du =...

sin of an angle θ is sinθ=p/h. again sin90=1 which means that p=h.but the hypotenuse is the longest side of a right triangle so how can it be equal to the perpendicular?

Homework Statement Im confused about something. Ill post the answer sheet to a question. It has all the data you need. BELOW: NOW... for Tangential component of the acceleration, WHY did they pick cos? and for Radial, WHY did they pick sin? I am starting to do a lot of FBD to equations...

So all I'm trying to do is plot y = (2sin(3w))/w, w is the angular frequency. I basically want this graph in radians. So this is what I did at first: >> x = [0:.01:20] ; //want bounds from 0 to 20 y = 2.*((sin(3.*x))/x); plot(y) But when I do this I get a graph of nothing, I assumed...

Homework Statement Leta theta be the angle between the vectors u=2i +3j -6k and v=2i + 3j+6k A) use the dot product to find cos theta b) use the cross product to find sin theta c) confirm that sin^2(theta) + cos^2(theta)=1The Attempt at a Solution I got a to be 117 degrees, but however b and c...

Homework Statement derive the formula inverse sinhx = ln(x+sqrt(x^2+1)) for all real x Homework Equations sinhx=(e^x-e^-x)/2 ? The Attempt at a Solution i have been staring at this for awhile and i don't know how to start what should be the first step towards deriving that...

I am very much confused and frustrated at this point and would just like to understand what I'm doing wrong... This program is supposed to calculate a truncated value of sine using it's series expansion beginning at i = 1. At values under 20 degrees it compares almost exactly with the intrinsic...

1. ∫ 6e^(-y/4) dy 2. ∫ [ sin(pi x) - (3/x) ] dx Any help with either of these would be great. I'm teaching myself integrals for Physics C and i have absolutely no clue what to do with these. Thanks in advance

I'm currently reading Apostol's Calculus. I'm now on the part where I need to prove sin and cos values for specific values. Right now I'm working on sin and cos of pi/6. However, I always get at 1/2 and √3/2 for the final value. Here's my solution so far: Homework Statement Use the properties...

According to Wolfram Alpha, if sin x =cosh x then x=-(\frac{3\pi}{4}+\frac{3i\pi}{4}) But how do you derive this? Also, what is the solution to cos x = sinh x in exact form? Thanks.

Homework Statement If sin x + sin2x + sin3x= 1, then find out the value of cos6x-4cos4x+8cos2x. Homework Equations The Attempt at a Solution How should i start? :confused: I don't find any way to convert them to cos 6x or cos 4x.

Homework Statement limx->\pi/2(ln sin x)/((\pi-2x)2)Homework Equations The Attempt at a Solution Putting \pi/2 into this equation gives 0/0, however, the limit of this could be 1,0 or infinity, so how would you distinguish between the three?

Homework Statement integral (sin^4(x) + cos^4(x))^.5 dx Homework Equations sin^2(x) = (1 - cos^2(x)) The Attempt at a Solution cos^4(x) + {1 - cos^2(x)}^2 = 2cos^4(x) -2cos^2(x) + 1 subst u = cos^2(x) integral (2u^2 - 2u +1)^.5

Homework Statement For tan(theta) = /2/3 (theta in quadrant 2) find sin(pheta) and cos(pheta) using the pythagorean identities. Homework Equations The Attempt at a Solution Which 2 pythagorean identities would I use? My trouble is with finding sin and cos from tan.

Homework Statement Im doing a question where I have to graphc y = -4 sin x Ok well I got the period and amplitude, so I have the interval of [0, 2pi] Now, in order to plot points, I have to divide the interval into 4 sub intervals. I don't understand how I do that! This is where I...

Homework Statement Ok, this is not really a problem, but I need help on understanding the basics of sin, cos, tan, and their inverses. i was looking at http://www.analyzemath.com/DomainRange/domain_range_functions.html and it was saying that the domain for sin and cos is (-inf , + inf)...

Homework Statement y=-2+sin((\frac{\Theta}{3})-(\frac{\pi}{12})) Homework Equations The Attempt at a Solution [PLAIN]http://img715.imageshack.us/img715/7707/trigg.png Phase shift: \frac{\pi}{4} Vertical shift: -2 Period: 6\pi

Hi all, I work as monitor for a pre-university course and one student showed me this problem: Homework Statement To find how much is y: y=sin2(10)+sin2(20)+sin2(30)+...+sin2(80)+sin2(90) Homework Equations I don't know. I thought about sen2x+cos2x=1 The Attempt at a Solution To...

Hey guys! I'm trying to solve a 2nd order differential equation. I am quite familiar with the method of solving these equations like treat them like characteristic equation ODE. but there's a question which I really want to solve. question is d^2 X/dt^2 +dX/dt +sinX=0. How should I solve this??

Doing a past paper where long story short I have a set of equations and I have to prove the variables are equal to some trig function. Namely: a^2 + c^2 = b^2 + d^2 = 1 ad - bc = ab + cd = 0 Now I know that sin^2 + cos^2 = 1 and that sin(A+B)=sinAcosB + cosAsinB, etc and the...

Homework Statement Given a n-sided polygon. Divide it into multiple small triangles that have same radius r. Compute the following limits: Homework Equations The Attempt at a Solution When I plug in a random number to guess the answer, somehow it is always near 0 (very small) so...

Homework Statement Its a word problem but I will just state everything here in simple form. Given ------------ V initial = 100ft/s r=300ft r= 1/32 V^2 Sin 2theta Unknown --------- Solve for theta The Attempt at a Solution 300=1/32 (100)^2 sin 2theta 300= 1/32 (10000) sin 2theta 300= 312.5...

Homework Statement Solve sin z=2 by (a) equating the real and imaginary parts (b) using the formula for arcsin z. Homework Equations (a) sin z = sin x * cosh y + i * cos x * sinh y arccosh z = log[z + sqrt(z^2 - 1)] (b) arcsin z = -i * log [i * z + sqrt(1 - z^2)] The...

Ok... so I had this down and now I am all confused ;/ I am not posting in the homework sections because its not for homework although I will gie an example of a problem... I just want to understand why/how they use these to find the force/tension... Example: A 20 kg loudspeaker is...

Homework Statement This would be easier if I knew how to use LaTeX, but I'll give it a shot. Show by explicit integration that the following is true: Integral from 0 to a of sin(m*pi*x/a)*cos(n*pi*x/a)=0Homework Equations The Attempt at a Solution I've used an identity to change...

Homework Statement Sin^{2} 20\circ + 1/sec^{2} 20\circ = 1 ? Because isn't 1/sec the same as cosin? Homework Equations The Attempt at a Solution

Sin pi/12= 1/4 (√6 - √2) ? I took sin pi/12 = sin (4pi / 12 - 3pi/12) = sin (pi/3 - pi/4) Did I do this right?

Homework Statement I'm asked to derive equation(2) from equation(1). equation(1): d=(tsin(2i))/((n^2-sin(i)^2)^1/2) equation(2): n=sin(i)(((2tcos(i/d))^2+1)^1/2) Homework Equations The Attempt at a Solution My attempts have got me nowhere, and I don't know how to even...

Homework Statement This problem deals with the displacement of a light ray as it travels through a glass medium. Starting with the equation #1: d=S[sin(i)cos(r)-cos(i)sin(r)] (where d=the length of displacement of the light ray in the glass medium, i=angle of incidence...

Homework Statement Integrate sin5(x/3)dx on the interval [0,pi] Homework Equations sin2(x)=1-cos2(x) dcos(x)dx=-sin(x) The Attempt at a Solution I split off one of the sins and then set my integral equal to (sin2(x/3))2*sin(x/3) switching in 1-cos2(x/3) afterward. Then I set u =...

why does tanθ = 1/2 > 0 and sin θ" mean that it lies in quadrant 3 Homework Statement Given one value of a trigonometric function, and the sign of another, find the remaining ones Given that tanθ = 1/2 > 0 and sin θ < 0 , the point P = (x,y) that corresponds to θ , lies in quadrant 3 Homework...

Homework Statement The ratio sin theta =-12/13 Homework Equations The Attempt at a Solution which comes out to according to my calcuations -0.9230, i then use 2nd sin function on my calculator and come up with -67.3 degrees this answer is legitimate but another way of writing...

Homework Statement This is what my professor is asking me to do: Show a table for when sin(theta) and theta have a percent difference of 1%, 5%, and 10%. (i.e. this table will have three columns)" You are to show this table (for all three quantities) such that the behavior leading slightly...

Homework Statement This is a more general question... but here is a specific example in which I don't know why sin is used where it is and why cos is used where it is. I don't need the problem worked out or anything (I have it worked out by my professor), I just need to understand why sin and...

Homework Statement Why is sin x / x at x = 0 equal to 1? Homework Equations d/dx (sinc(x)) evaluated at x = 0. The Attempt at a Solution El hopital's rule Cos(x)/1, cos(0) = 1 However when looking at the picture of Sinc, http://www.wolframalpha.com/input/?i=sin(x)/x, it...

Ok... (2, -3) R = (Sqrt x^2 + y^2) R = (sqrt (2)^2 + (-3)^2) R= (sqrt 13)^2 R=13 Sin = y/r Sin -3 / 13 ? Cosin 2 / 13 ? But then.. how come the answer gives me sin -3 (sqrt13) / 13 and for cosin 2(sqrt13) / 13 My question is how come there's a (sqrt13) included for the...

I have a rather difficult math problem. In my circuits class the professor prefers to express the cosine function using Euler's formula as (ejwt+ejwt)/2. Last semester for the final, one of the problem's solutions (that he gave us) used partial fraction decomposition to solve the Laplace...

Homework Statement I have to fill in the missing info... Y=A*Sin[B(x-c)] +D A = 3. For finding the amplitude all I have to do it multiply 1/2 by the range? D = 3. For finding upward shift all I have to do is see if the center has moved up? period = 4pi/3 so B = 3/2 I am confused on...

find the first three non zero terms in the Taylor Series about z=0 of exp(z sin z) i have little idea how to even start on the question because it is exp to the power of z sin z and it just looks too complicated. i hav tried looking thru txtbooks for something similar but no similar question...

Find the derivative. d/dx \int\stackrel{x^5}{o} sint dt I came up with sin x^5. The answer is 5x^4 sin (x^5). Not sure what I'm missing here.

So I have a Hermite curve with the control points: //point# (x,y): p0 (1,0) p1 (1,(Math.sqrt(2)-1)) p2 (Math.sqrt(0.5), Math.sqrt(0.5)) I also have a very basic algorithm to find the point on the locus at a given degree between 0 and 45 degrees using the control points. I could...

It seems to me that the standard definition of the complex Arcsin (the principal branch) is something like this: [PLAIN]http://math.fullerton.edu/mathews/c2003/maptrigonometricfun/MapTrigonometricFunMod/Images/mat1017.gif Anyways, it's defined as a map from C-{z in R : |z|>=1} to the strip...

Homework Statement prove that for all x>0 Homework Equations -1 \leq sin t \leq 1 The Attempt at a Solution the area under the graph is increasing as x increases also, i tried to write it the sigma way: then take the limit as n-->infinity i got stuck trying to figure out how to...

Hi, I am in calculus and am having major struggles. If someone could provide a walk through on how to answer these questions, that would be fantastic. Cheers! Let f(x)=−3x+6 if x<-3 = 15 if x > -3 Find the average rate of change of f(x) on the interval −5<x<5 . The average rate of...