What is Trig: Definition and 1000 Discussions

If I wanted to integrate \int \sqrt{1+x^2} dx, I would let x=\tan\theta , which implies dx=\sec^2 \theta dx so that I would have: \int \sqrt{1+x^2} dx = \int \sqrt{1 + \tan^2 \theta} \sec \theta d \theta = \int \sqrt{\sec^2 \theta}\sec^2\theta d\theta = \int \sec^3 \theta d \theta It is...

Homework Statement Given that \frac{d}{dx} (\text{arccot}{x}-\arctan{1/x})=0 \hspace{10mm} \forall x \ne 0, prove that there is no constant C such that \text{arccot}{x}-\arctan{\frac{1}{x}}=C \hspace{10mm} \forall x \ne 0 and explain why this does not contradict the zero-derivative theorem...

I'm looking for a source online that gives the step by step derivation of common trig identities, such as sin(2theta) = 2sin(theta)cos(theta), cos(2theta) = cos2(theta)-sin2(theta), sin2(theta) = (1 - cos(2theta))/2, ect. I did do 20 minuntes or so of searching online, nothing was exactly what I...

Does Apostol ever introduce "Trig Substitutions"? I took Calculus before, but I am going over Apostol's Calculus Vol. 1 book. In section 5.7 he introduces Integration by Substitution, but never really discusses what was commonly referred to as "Trig Substitutions" in my Calc classes. For...

Homework Statement \frac{sin\theta}{1-cos\theta} - \frac{cot\theta}{1+cos\theta} = \frac{1-cos^{3}\theta}{sin^{3}\theta} Homework Equations Trig identities.. The Attempt at a Solution Basically I got to: \frac{sin\theta+(cos^{2}\theta)(sin\theta)}{sin^{2}\theta} Homework...

Hey guys, I'm currently a freshman at my local community college. I felt the need to solidify my foundation in Trig so I am currently doing a self-study course. The question is from I.M Gelfand's book on Trigonometry. Chapter 0, page 9, exercise 8. 8) Two points, A and B, are given in...

Homework Statement The first problem I'm having difficulty with is \stackrel{lim}{x\rightarrow0} \frac{sin x}{5x} And the second is: \stackrel{lim}{x\rightarrow0} \frac{sin x(1-cos x)}{2x^{2}} Homework Equations I assume that for the first problem I need to simplify it to the rule...

I was reading on planetary motion and have gotten hung up on a "rearrangement of terms" that the author skimmed over. It reads that: r=e(k+rcos(θ))=(ek)/(1-ecos(θ)) It's been a while since I've been in a math class: I just can't follow how to get from a to b. Is there anyone who can walk...

Homework Statement tan^-1(x/(1-x^2)^1/2) find the derivative the problem comes from 3g from MIT's PDF I found http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-b-implicit-differentiation-and-inverse-functions/problem-set-2/MIT18_01SC_pset5sol.pdf...

Homework Statement evaluate lim(x->0) (tan^8(t))dt(between 0 and sin^2x) Homework Equations The Attempt at a Solution [tan^8(sin^2(x))]/sin^18(x) my book says to use l'hospital's rule, so i continued with [8tan^7(sin^2x)*sec^2(sin^2(X))*2sinxcosx] but my book says i should...

Homework Statement I'm doing a optimisation question and I get to a point where I have to verify a maximum using a double derivative and I need to differentiate -5sin^2(x) Homework Equations -5sin^2(x) The Attempt at a Solution -10cos(x)sin(x) I am not sure if the answer is positive...

Homework Statement the amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain day in may in the city of long beach is appoximated by: A(t) = ((544) / (4 + (t - 4.5)^2) + 28 t is on interval [0, 11] where A(t) is measured in pollutant...

Homework Statement Which one is not periodic? (a)|sin 3x|+sin2x (b)cos\sqrt{x}+cos2x (c)cos 4x + tan2x (d)cos 2x+sin x Homework Equations The Attempt at a Solution I don't understand how to show whether the functions are periodic or not? :confused:

Homework Statement \int\frac{sec^{2}x}{tan^{4}x}dxHomework Equations The Attempt at a Solution I have the answer as -1/3 cot^3(x) + C listed. All the intermediate steps are given, but the first one is they have converted the sec/tan integral in to: \int{cot^{2}x}{csc^{2}x} dx I am a little...

I was calculating some numbers, revolving around a sphere and some integration. The case was to find out for what x-value a spherical bowl with a radius of 5m was half filled. After doing the algebra, I narrowed it down to x^3 - 15x^2 + 125 = 0 Now, my calculator says that the solution...

I need a basic math formula with the following properties: * limit y between -1 and 3. * (x, y) hits (-1, 0), (0, 1) and (1, 2). * Each y value occurs only once. I managed to do this with y=4/pi*ArcTan(x)+1. But I'd like to do this without trig. I got close with y=x*2/SQRT(1+x^2)+1. But...

Homework Statement tan^2x - sin^2x = sin^2x*tan^2x Homework Equations The Attempt at a Solution This is how my teacher solved it. Sin^2x sin^2x ______ - ______ Cos^2x 1 sin^2x - cos^2x*sin^2x _________________________ cos^2x = sin^2x (1-cos^2x)...

Hi Not sure if this is simple or not but I can't figure out how to do it! I am designing a surround that will be constructed by folding a sheet of aluminum. I've got the geometry right in 3d but I want to transpose this to a template. Yes I can measure but I want to solve using maths for...

Homework Statement let g be a function mapping x to xcosx-sinx. use the mean value theorem to prove that g(x) < 0 for x in (0,pi]Homework Equations well the function is both continuous and differentiable on the interval so that's a start... The Attempt at a Solution basically i thought i'd...

Homework Statement I don't understand how to solve for these, I will post 3. d) [sqrt]2sin x + 1 = 0 (sqrt only over the 2) e) 2cos x - [sqrt]3 = 0 f) 2sinx +[sqr]3 = 0 Esentially, I don't understand how to get the degrees. I don't get how you use the terminal arm to predict the...

Homework Statement Prove this identity m) Sin^2 x / sin^2 x + cos x^2 = tan^2 x / 1 + tan^ x Homework Equations http://i52.tinypic.com/105tdtk.jpg Letter (m) on the top The Attempt at a Solution I don't know to much about trig identities, he barely taught anything. But...

Homework Statement This question has me stumped Please help me get this monster completed. Compute the definite integral of -2011 to 2011 of (1+sin^2(17t))^2011*sin(sin(-t))dt Homework Equations The Attempt at a Solution

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Homework Statement Prove that: (sin(x)+ tan(x))/(cos(x)+ 1)= tan(x) Homework Equations There are just trig identities that we can use.The Attempt at a Solution I've attempted every possible way I can think of and it would just look like jibberish here.

Homework Statement A cargo ship is tied up at the dock. At low tide, a 12-m long unloading ramp slopes down from the ship to the dock and makes an angle of 30 degrees to the horizontal. At high tide, the ship is closer to the dock, and the unloading ramp makes an angle of 45 degrees t othe...

Trig...should I start by squaring both side? Homework Statement Fing the solutions that are in the interval [0,2\pi) \tan 4t-\tan 7t=1+\tan 7t\tan 4t Homework Equations Use an addition or subtraction formula. \tan(a+b)=\frac{\tan a+\tan b}{1-\tan a\tan b} The Attempt at a...

Homework Statement tanx+secx=1 Homework Equations The Attempt at a Solution tanx+secx=1 tanx=1-secx then square both sides? \tan^2 x= 1-2\sec x+\sec^2 x\sec^2 x-1=1-2\sec x+\sec^2 x2-2\sec x=0\sec x=0 No Solution

Homework Statement SinA is = to -3/5 with A in Q3, find sinA? Homework Equations The Attempt at a Solution When I did this I set it up like First find cosA So to do that I used plus/minus √(1-sin^2A) The problem is that I really got confused when plugging in the values under...

Homework Statement 8cos2\theta-4\sqrt{3}=0 Homework Equations I don't have one. The Attempt at a Solution I am really not sure where to begin, our lesson tonight was lacking detail. I guess start by addding 4\sqrt{3} to the right side Then what? I don't think I should...

Hi, This is just a part of a calculus 1 problem. It occurs while attempting to make f'(x) = 0 f'(x) = cosX - 1/6cos3X Now to make this zero I quickly note that in the domain of (0-2pi) cos=0 at pi/2 and 3pi/2 so the expression equals zero already! I have been informed by my instructor...

What programs should I download on my TI 89 for trig? Where do I get them? Where can I find all of the trig programs that are all ready on my TI-89? Can I find the arc length on circles and stuff like that with it the way it is?

Homework Statement [cscx/(1+cscx)] - [cscx/(1-cscx)] = 2 sec^2 x Homework Equations prove the left side equals the right side The Attempt at a Solution 1. get common denominator and subtract, [cscx(1-cscx)-cscx(1+cscx)]/[(1+cscx)(1-cscx)] 2. distribute cscx in numerator...

Homework Statement -sin pi/4 , give the exact value? -1/root 2 is the answer according to the book? How in the world do they get that result. What do you to make that happen? Homework Equations The Attempt at a Solution Also, is this how to do the problem? Find pi/4 on the...

Trig function:-sinx+(1/2)sin2x(2) The criticial points are (pi), (pi/3), and (5pi/3). Am I correct?

Hey guys these aren't math exercises; I just don't understand a couple parts in my textbook. 1. Cos(x)/Sin(x) = Cot(x), but Cot(x) * sin(x) ≠ cos(x). Why? I know tan(x) * sin(x) ≠ cos(x) because during precalculus nobody ever used sin(x) * cot(x) = cos(x) for anything, but I don't know why you...

I tried doing this problem but I don't think it is right can someone help me? 2(sin(x))^2+3sin(x)=-1 over the interval [0,2pi)

Just wondering what you find harder? Trig or Calculus?

Trig Question: Exact value of ... Homework Statement Find the exact value of: sin(11"pi" / 2) without a calculator... Homework Equations The Attempt at a Solution I don't understand how to solve this with the unit circle. What is my first step here?? My textbook just...

Homework Statement I've come across integrals of exponential and trig functions and I have no idea how to do them. Integration by parts doesn't really work because they just derive into either e or another trig function. One of them is \intsin(a)*sin(b - a)da Another is \inte(a)*sin(a)da...

So this is not an homework question, and I have solved the integral... Just it took a lot of time and was very tiresome. A quick outline on how I did it. I mainly used two formulas \sin(A)cos(B)=\sin(A+B)+\sin(A-B) \sin(A)\sin(B)\sin(C)=\frac{1}{4} \left[ \sin(A+B-C) - \sin(A-B-C) +...

Homework Statement Prove: cotAcotB=(cscB+cotA)/(tanAsecB+tanB) Homework Equations cotx=1/tanx, etc. I tried using pythagorean identities, like 1+cot2x=csc2x, and others, but I've been unable to solve the problem. The Attempt at a Solution Please help me out. The examples in my...

Homework Statement I have to prove the following: \int_0^{2\pi} \frac{\mathrm{d}\theta}{(a + cos(\theta))^2} = \frac{2pia}{(a^{2}-1)^{3/2}} for a > 1. Homework Equations I have an example at hand for \int_0^{2\pi} \frac{\mathrm{d}\theta}{a + cos(\theta)} from which I know I have to...

Homework Statement Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution θ (see the...

Homework Statement 3-2csc(x) = 17 Homework Equations N/A The Attempt at a Solution 3-2csc(x)= 17 -2csc(x) = 14 csc(x) = -7 cscˆ-1(-7) = x x = -.14 radians. This is not the correct answer. The correct answerS ARE 3.28 or 6.24 radians. I am beyond confused. Please help :)...

Homework Statement This isn't really a question on its own, rather a step in the solution to another question: How would I prove that y= A\cos x + B\sin x (A, B arbitrary constants) has at least n zeroes in the interval [\pi , \pi (n+1)] where n\in\mathbb{Z}\;? (I don't need to be too...

Homework Statement Integrate: \int \frac{1}{(3+2cos(θ))} dθ evaluated from zero to pi. Homework Equations I can't think of any. All of the integration formulas in the text rely on the existence of a singularity somewhere in the complex plane. This thing is analytic everywhere...

Homework Statement Prove the Identity (show how the derivatives are the same): arcsin ((x - 1)/(x + 1)) = 2arctan (sqr(x) - pi/2) Homework Equations d/dx (arcsin x) = 1/ sqr(1 - x2) d/dx (arctan x) = 1/ (1 + x2) All my attempts have been messy and it may be because I didn't...

Homework Statement Does this look correct? How do I know when to stop simplifying things? Sometimes it comes out to a nice little expression, and other times it's a long solution. In the latter, I spend too much time trying to simplify it further! Homework Equations The Attempt at a...

Homework Statement Differentiate: y= u(a cos(u) + b cot(u)) Homework Equations No Chain Rule The Attempt at a Solution I started out finding the derivative of (a cosu + b cotu) I'm guessing that a/b is constant? \frac{d}{du}(a cos(u) + b cot(u))= =(0(cosu)+a(-sinu))+(0(cosu)+b(-csc^2u))...

This is from Griffiths page 446. In radiating dipoles: V(\vec r,t)=\frac 1 {4\pi \epsilon_0} \left [ \frac {q_0 cos [\omega(t- \frac {\eta_+} c )]}{\eta_+}- \frac {q_0 cos [\omega(t- \frac {\eta_- } c)]}{\eta_-} \right ] Given conditions d<< \eta\; and d<< \frac c {\omega} ...