Trigonometric Definition and 1000 Threads

Hi, I'm having trouble understanding how my math book factored the following equation. [(cos(t)sin(t) - (1 + sin(t))cos(t)) / (cos(t)cos(t) - (1 + sin(t))sin(t))] to get [(cos(t)(1+2sin(t))) / ((1 + sin(t)) (1 - 2sin(t)))] I get the numerator but I don't understand what happened...

hey I have this question and have looked it up in the textbook and web sites but can't seem to find what to do! Any assistance would be appreciated thanks! Find the first derivative w.r.t the relevant variable 5^(sin(theta)) I am guessin the relevant variable is theta but I don't even no...

Hi. Are there any addition theorems for inverse trigonometric functions? Like arccos(x+y)=? or something... I was wondering about this when I tried to find the derivative of f(x)=arccos(x) by setting f'(x)=\frac{\arccos(x+\Delta x)-\arccos(x)}{\Delta x}

Hi, I have an exam on trig integrals tomorrow and need to freshen up on some basic trig rules (i.e. d/dx of sin(mx) and trig identities such as sin^2(x)+cos^2(x)=1) I was curious if anyone new of some good websites that reviewed all common trig identities used in calculus. Any help is...

Alright, moving on to the topic of taking the derivative of a trigonometric equations, I have been given the problem to find the equation of the tangent line to the curve at the given point for: y = 1/sinx+cosx at (0,1) Now we know that the equation is y-1=m(x-0), so I've tried solving for...

need some assistance with the following integral: \int_0^{2\pi} cosx/(a-cosx), a-parameter (say a>0) i've converted it into a complex contour integral over z=e^(ix): ~ \int_{|z|=1} dz (z^2+1)/[z(z^2-2az+1)] which is easily evaluated for a>1. my question regards a<1 - i am not sure...

Find dy dx 1.) y = In __x2 (x+1)___ (x + 2)3 2.) y = x3 ( 3lnx-1) 3.) y = __cos6 2x__ (1-sin2x)3 4.) y = __tan 2x__ 1- cot 2x 5.) y = x e (exponent pa po ng e) sin2x 6.) Arc tan...

Hi, I have a question about a problem: 1/2csc(THETA)sec(THETA) I have to find the identity for it and I know that csc is 1/sin and sec is 1/cos but after that I don't see where it can lead to a simple answer. If anyone knows it would be helpful, thanks!

Hi. I have to show that x(t)=c1 cos(wt) + c2 sin(wt) '(1)' and x(t) = A sin(wt + phi) are equivalent. I know I have to use sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) or cos(alpha +beta)= cos(alpha)cos(beta) - sin(alpha)sin(beta) I have been strugling with this...

hey just wonderin if any1 could give me a hint as to the best method to prove the following trigonometric indentity: sin^4x-cos^4x = 1 - 2cos^2x i tried the side more complicated first...but can't seem to hav any luck...other then maing it more complicated! umm the x's are meant to be...

Solve the following equation giving values from -\pi to \pi: cos (2v - \frac{\pi}{3}) = \cos v Here is my attempt to solve it. As the cosine of the two is the same, the angles should also be the same leaving 2v - \frac{\pi}{3} = v + 2 \pi n Then if I move the right over to the left, I get...

just looking at another question to do with trigonometric functions and I can't see how they simplify the follwing: 2sin^2x-3sinx-2=0 to (2sinx+1)(sinx-2)=0 again i prob thinking sumthin really stupid...but i can't see wat! cheers

I'm working on a pre-freshman year math packet for college, and at one point it asks for the derivative of sinh-1(x), followed up by the derivative of ln( x + sqrt(1+x2) ). In high school, we never really covered hyperbolic trigonometry, but I have previously derived that the inverse of sinh is...

Let be the series: \sum_{n} e^{if(n)} where f is a function perhaps a Polynomial ..then my question is..how can this series to be evaluated (at least approximately) ?..perhaps using Euler-Bernoulli sum formula, and another question what are they used for?, i heard in a book that Goldbach...

as we know that (sin(x))^2 + (cos(x))^2=1 how about (sin(3x))^2 + (cos(3x))^2 and 5sin(3x)^2 + 6cos(3x)^2?? how can we solve these problems?? thanx

Cud u Help Me How to Graph these? y = 2 + sinx ; where x = teta y = 2sinx ; where x = teta cud u give me some ideas pls?

These are some equations that I recently developed and submitting for review. Evaluations?, comments? Iterated trigonometric differentiation: \frac{d^n}{dx^n} \sin x = \sin \left(x + \frac{n \pi}{2} \right) \frac{d^n}{dx^n} \cos x = \cos \left(x + \frac{n \pi}{2} \right) Iterated...

Hey guys, I have to know how to Differentiate Inverse Trigonometric Functions in my next exam and need somewhere to study up on them. Do you know of any web sites I could read? Can't find anything on Karl's Calculus. Thanks

Dear all, How to solve this trigonometric equation systematically? 2cos^(2) x - cos x = 0, where x ∈ [0,360] Thanks in advance

Hi guyz, as we know we have some known relations in the trigonometric functions like sin(2x)=2sin(x)cos(x) and sin(x/2)=1/2-1/2 cos2x My question is are there similar formulas for arcsin and arccos? I know those only ! arcsin x =ln(ix-sqrt(1-x^2)) arccos x =ln(-ix-sqrt(1-x^2))...

I'm having some trouble with applying trigonometric functions to some real life situations, particularly this one problem in my homework. Andrea, a local gymnast, is doing timed bounces on a trampoline. The trampoline mat is 1 meter above ground level. When she bounces up, her feet reach a...

Haven't done integrals in such a long time and now I'm having some trouble with this question here. Any help would be appreciated. Thanks :smile: http://img331.imageshack.us/img331/4333/screen192cj.jpg

I have stuck on this problem for long time sin^2 \alpha = \frac{\alpha}{2} I never meet this kind of problem before, and I have no idea about this. Could someone tell me how to solve this kind of problem? Thanks in advance. (Ans: \alpha = 1.39 rad )

Trigonometric Identity?? I just can't figure this out. I don't think I've covered enough material to do this. Can anyone help? I've put the entire question but I am sure all i need is a little explanation and maybe the first answer and i could do the rest. :confused: Let z =...

x_1(cos\alpha-1) + x_2sin\alpha = 0 x_1sin\alpha + x_2(-cos\alpha-1) = 0 How to solve this equation? Can anyone help me?

What other curves are there that cannot be described by the above? Are trigonometric functions actually a special case of exponentials with complex powers?

My Pre-Cal teacher gave us this problem today. I have worked on it for a very long time and have goten no where :confused:. I was wondering if anyone had any ideas on how to do it, or even where to start. I started it myself with using the pythagorean idenities for the left side, then the...

Hi, i need help with simplifying this problem. I think it is an identity, but it looks very complex, and I wanted some other peoples thoughts/opinions. Well here goes... cos^2((pi/4)-(x-2)) - sin^2((pi/4)-(x-2)) I reduced it using the identity cos2x=cos^2x - sin^2x. I came out with...

I have a question when solving trigonometric equations. For example: Find all the solutions in the interval [0,2pi) \sin \theta \tan \theta = \sin \theta \] If you choose to divide through by \sin \theta\] we get, \tan \theta = 1\] such that \sin \theta \ne 0\] otherwise we are...

I'm having trouble with two problems: 2tan(x) - 2cot(x) = -3 and cos(x)^2 + sin(x) = 0 On the 2nd one, I can substitute 1-sin(x)^2 for cos(x)^2 right? I tried that, but it didn't work. And I have no clue what to do on the first one. Little help please?

In the same way that it is possible to derive most trigonometric identities from the addition formulas, what is the way that the difference of sines and cosines formulas were derived, such as \sin{a}-\sin{b}=2\cos{\frac{a+b}{2}}\sin{\frac{a-b}{2}} thanks, I am trying to avoid as much...

the two problems are the integral of (sec^3x)(tan x)dx and the integral of (sec^4x)(tan x)dx will substitution work for both of these problems

A circular cone is inscribed in a sphere with a radius of 30cm. The semi vertical angle is theta. Derive a trigonometric equation for the volume of the cone. This has be stumped. I tried looking up proofs for the expression of the volume of a cone for inspiration but all involve calculus.

Question: lim(x->0) for (tanx - sinx) / (sinx)^2 This is what I got: = (sinx-sinxcosx) / (cosx)(sinx)^2 = (sinx)(1-cosx) / (sinx)(sinx)(cosx) = (1 - cosx) / (sinx)(cosx) However, I can't figure out what to do from this step, as the limit still equals 0/0 at this stage.

Question: lim(x->0) for (tanx - sinx) / (sinx)^2 This is what I got: = (sinx-sinxcosx) / (cosx)(sinx)^2 = (sinx)(1-cosx) / (sinx)(sinx)(cosx) = (1 - cosx) / (sinx)(cosx) However, I can't figure out what to do from this step, as the limit still equals 0/0 at this stage.

Problem: \int sin^6 x dx Progress so far: \int (sin^2 x)^3 dx \frac{1}{8} \int (1-cos2x)^3 dx \frac 1 8 \int (1 - 3cos2x + 3cos^22x - cos^32x) dx Any help is appreciated. I can see using a half angle identity for cos^2(2x), but what do I do with the cos^3(2x)? Steve

As I rack my brains to solve(or atleast pretending) to prove Trig identites. What is it application in real life? :cry:

f(x)= sin 3x - (1/2)sin x, find the period. i know the period for sin 3x is 2pi/3 and the period of sin x is 2pi but how do you subtract these? I totally forget how to do this! I mean i could find the answer with any graphing program but i want to know how to do this type of problem.

How do I get from the primary to the secondary solution of a trigonometric equation? This book tells me that the second angle is within -\pi \leq \theta \leq \pi, in a different quadrent, but I don't follow :\ Thanks. Edit: I got it (I think!): I can pick the correct quadrent using the...

Hello all, I have been looking up the golden ratio and found most of what I needed on mathworld. The site states that \phi \ = \ \frac{1}{2}(1+\sqrt{5}). I can see how (despite the fact that I don't understand how the ratio: \phi \ = \ \frac{AC}{BC} \ = \ \frac{AB}{AC} is formed but...

When y=sin(pi*x), why does y'=cos(pi*x)*pi, not y'=cos(pi*x)? hk

I am looking for help in solving a pair of simultaneous equations. I have not come across any maths book that solves trigonometric ones. I was wondering if I could get a step by step solution. Thanking you in advance for your time: 5.4=10cos(x) + 13.41cos(y) ....(i) 0=10sin(x) +...

Hello, I'm in need of a hint or few pointers on how to calculate the angle C of the picture attached. I've already calculated y. I was doing a few problems in this Dynamics book, i bought recently, and the ascention angle (angle C) is beating me :eek: "The airplane C is being tracked...

I have a math test on the chapter on Tuesday, and my teacher handed out the pre-test on Thursday. There are a few problems I am totally stumped on, and figured the math geniuses here could give me some help. Some I can get somewhere with, some I don't know where to begin. Here is one...

Hello everyone, I am having some trouble with an integral. \int \sqrt{x^2 - 1} dx so far: x = sec \theta \frac{dx}{d \theta} = sec \theta tan \theta dx = sec \theta tan \theta d\theta now we substitute: \int \sqrt{x^2 - 1} dx = \int \sqrt{sec^2 \theta - 1} sec \theta tan...

Here's a integral where I have to use trigonometric substitution but I can't get the right answer. [int a=0 b=3] 1/(sqrt[9-x^2]) dx I did the limit as t approches 3 from the left. Then i did my trigonometric substitution, and it gives me arcsin(x/3). Then i computed what i had...

How would you solve for \alpha in the following equation? 4=\cos(\alpha)+\cos^2(\alpha)+\cos^4(\alpha)

The problem reads: Find \sin\theta and \cos\theta Part a gives me the coordinates \left(-1,1\right) The triangle I got had the x-length as -1, while the y-length was 1. The hypotenuse I got was \sqrt{2} Since \sin is \frac{opposite}{hypotenuse} I got \sin\theta=\frac{1}{\sqrt{2}}...

\int x^3\sqrt{4-9x^2}dx I tried to use x=\frac{2}{3}\cos{(x)} but it just left me with \int \sin^3{(x)}\cos^2{(x)}dx Any suggestions? Thanks for your help.

The math book I have does a pretty terrible job explaining this to me, because I am absolutely stumped as to why I get every question wrong in two sections: finding values of each expression in radians (can often be given in terms of ?) and finding approximate/exact values of the expressions...