Trigonometric Definition and 1000 Threads

Homework Statement 1) lim sin^2(3x)/x^2 x->0 2) lim 2sin5x/(3x-2tan2x) x->0 Homework Equations lim sinx/x = 1 x->0lim tanx/x = 1 x->0 The Attempt at a Solution We just began working with limits, and we haven't covered much of trig functions at all, but our prof gave us...

Homework Statement This may be basic, but how do you know which part of an integration problem fill the up the triangle values for trig substitution?

while solving trigonometric equations many times we get answer in different forms depending on the way in which we solve the problem , so what is the best way to ascertain that all the answers are the same ?? pl. help!

Homework Statement Which of the following is not a possible solution of 0=sinθ+cosθtan^2θ? A. 3pi/4 B. 7pi/4 C. 2pi D. 5pi/2 Homework Equations All trigonometric identities. The Attempt at a Solution Too much to write down, at least two pages long, but I've been trying to...

Homework Statement lim x-> 0 ( sin(5x) - 3x ) / ( 3x ) Homework Equations (a - b) / c = (a / c) - b The Attempt at a Solution (1/3) lim x->0 ( sin(5x) / x ) - 3x = (1/3) lim x->0 ( sin(5x) / x )( 5 / 5) - 3x = (5/3) lim x->0 ( sin(5x) / 5x ) - 3x = (5/3) * 1 - 3x = (5/3) - 3x = (5/3) I...

Homework Statement Find the limit of sin(1/x) as x -> 0, I don't really understand why there isn't a limit, wouldn't it be +/- 1? or it doesn't exist because there are two values? I just need a more thorough explanation of the answer really.

Homework Statement Calculate the integral \int\limits_0^{\infty} \cos{x^2} dx This is the exercise from complex analysis chapter, so I guess I should change it into a complex integral somehow and than integrate. I just don't know how, since neither substitution cos(x^2) = Re{e^ix^2} nor...

I'm reading through a solution to a problem and at one point the following identity is used: \frac{1-\cos(\beta)}{\sin(\beta)}=\frac{\sin(\frac{\beta}{2})}{\cos(\frac{\beta}{2})} I've been trying to figure out where this comes from but with haven't got it yet. Any ideas?

I've read a bit about constructibe polygons, and that a regular n-gon can be constructed with compass and straightedge if and only if trigonomatric functions of 2π/n can be expressed with square roots and basic arithmatic alone. That is possible if and only if n is the product of distinct Fermat...

Homework Statement Prove: secA(1+sinA) = (1+sinA+cosA)/(1-sinA+cosA) Homework Equations I have the following equations: sin2x + cos2x = 1 1 + tan2x = sec2x 1 + cot2x = csc2x sin(A+B) = sinAcosB + cosAsinB sin(A-B) = sinAcosB - cosAsinB cos(A+B) = cosAcosB - sinAsinB...

Hey guys. How are you all doing? I'm helping my younger brother out with his trigonometry homework. He is dealing with verifying trigonometric identities. However, he has the problem that I am getting nowhere with. Hope you all can help. Thanks in advance. :) Homework Statement Verify...

Homework Statement http://d.imagehost.org/view/0659/Capture Link to wolfram alfa:http://www.wolframalpha.com/input/?i=integrate%28cos%28e^x%29*e^x What i don't understand is why whey do it like this and why i can't integrate by parts in this case? Thanks for any replies!

Hello, What's the easiest way to evaluate an integral like this? \int_{\frac{-\pi}{2}}^{0}\cos^{10}x dx The only method I can think of is to expand the \cos^{10} x using trigonometric identities, and getting \frac{1}{32}\left(1-\cos2x\right)^5. I tried subbing u=1-\cos2x but I doesn't seem to...

Homework Statement find the dy/dx of y = Sin4 x2 - Cos4 x2 Homework Equations derivatives and identities factoring dy/dx (Sinx) = Cosx dy/dx (Cosx) = -Sinx The Attempt at a Solution y = (Sin2 x2 - Cos2 x2) (Sin2 x2 + Cos2 x2) im stuck at this part i don't know how to...

Homework Statement y=(sin2x)(cos2) Homework Equations Product Rule for Derivatives identities: derivatives of Sinx = Cosx Cox = -Sinx The Attempt at a Solution i used the product and chain rule for derivatives then do the identities y = sin2x*cos2x dy/dx = (Cos2x)(2)...

Homework Statement \int_0^1 \! 7x\sqrt{x^2+4} dxHomework Equations The Attempt at a Solution Noticing that the radical is of the form x^2 + a^2, I know to use a*tan\theta. x = 2tan\theta dx = 2sec^2\theta d\thetaThen I simplified the radical to put it in terms of a trig function...

Homework Statement \int \frac{4}{x^{2}\sqrt{81-x^{2}}} dx Homework Equations The Attempt at a Solution Since the radical is of the form a^2-x^2, I'm using the substitution x=asin\theta. x = 9sin\theta dx = 9cos\theta d\theta Using this x value, I solved the radical...

This is supposed to be a proof of trigonometric multiplication of complex numbers: What happened at the =...= point? I understand everything up to that.

Homework Statement \int sin^6(x)cos^3(x) dx Homework Equations cos^2(x) = 1-sin^2(x) The Attempt at a Solution Since cos has an odd power, I took one out to make it cos^2(x), which can be used in the identity above. \int sin^6(x)cos^3(x) dx \int sin^6(x)(1-sin^2(x))cos(x) dx...

Hello, I have been an avid reader of the physics forum, and now I think I finally have something worth asking. The problem is engineering-related, but it all comes down to a trigonometric equation, so I'm posting in general math. The problem is the following: \frac{1}{N^2}...

Here's the equation: ∫(sqrt(2),2) (1/(x^3*sqrt(x^2 - 1)) I have the entire indefinite integral worked down to this (using x = a*secø): ø/2 + 1/4 * sin2ø Now I have the answer book, so I know that's right so far. What I don't understand is how it converted the points of the integral...

Homework Statement Find the second derivative (y") of y=xtanx. The attempt at a solution I got the first derivative (y') y=xtanx y'=x(secx)+tanx I started the second derivative and got stuck y"=xsec^2x+tanx

Is there any general and hopefully 'easy' way to find the trigonometric ratios of any angle? That is without using the sin, cos etc tables? If not any angle ... atleast whole number angles?

Homework Statement prove the identity. ln csc(x) = -ln sin(x) The Attempt at a Solution With a calculator I am able to prove it is in fact an identity, but I have NO clue why? In fact I am quite unclear on logarrithms in general as my algebra class just barely covered them and...

is there any definite way of finding the period of non trigonometric functions? can we use f(x+t)=f(x) and solve for t from this equation?

Homework Statement Find the limit as x approaches zero of xcsc4x = the numerator over cos17x = the denominator Homework Equations The Attempt at a Solution I don't know how to start except maybe multiplying both numerator and denominator by 4

I have been having lots of trouble verifying trigonometric identities. I know the fundamental identities but I am actually having trouble with the algebra that goes along with the problems. The problem I am working on now is: cos(x)-tan(x)/sin(x)cos(x) = csc^2 (x) - sec^2 (x) (The csc...

Homework Statement lim (sin 2x)/(sin 5x) x->0 Could someone please help me get started, I simply can't figure this one out. Homework Equations The Attempt at a Solution

Homework Statement Evaluate the definite integral of function dx/x^2+1 on interval [tan(3), tan(6)] Homework Equations The Attempt at a Solution The trigonometric inverse function for dx/x^2+1 is arctanx+c. I plugged in tan(3) and tan(6), and subtracted arctan(tan(3)) from...

Trigonometric substitution - Why? Hey guys Im sitting here with trigonometric substitution problems, and I have a kind of a problem. I can't see WHY it is legal to substitute x for a sin (\theta) If you have a the integral: \int\frac{1}{\sqrt{1-x^2}}dx Then I know the substitution would...

Hi, I am seeking some input for an integral I have been stumped on for a few days. This is the integral: [(a^2 - s^2)^1/2]/(x-s) ds evaluated over the bounds from -a to a. The symmetry of the integration area allows the integral to be evaluated from 0 to a, and doubled. I have always...

Homework Statement I want to express sin(x) in terms of tan(x).Homework Equations tan(x)=sin(x)/cos(x) 1+tan2(x)=sec2(x)The Attempt at a Solution sin(x)=cos(x)tan(x) At this point I realize this is assuming x\neq \pi/2+k\pi cos^2(x)=\frac{1}{1+tan^2(x)} therefore...

Homework Statement I'm trying to integrate the following form: y = \int e^{\sin x} dx The Attempt at a Solution I thought about trying to write something like: y = \int e^{\frac{i}{2}e^{-ix} - \frac{i}{2}e^{ix}} dx But this seems to lead down the road of trying to integrate...

I got these two questions wrong and I'm wondering what i did wrong. Homework Statement [/b] 1. http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q3.jpg 2. http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q4.jpg The attempt at a solution[/b] 1...

Homework Statement I got this expression while solving a problem. (y+1)/(y-1)=sin2x/sin2a we need to find the range of y Homework Equations The Attempt at a Solution here y=(sin2x+sin2a)/(sin2x-sin2a) Numerator of RHS lies between sin2a-1 and 1+sin2a Denominator lies...

Hi. I'd like to know whether is it possible to do the following, and if so, how...(and also, whether is it possible to solve similar problems) I have parametric equation of a curve and I need to find its intersection with a ray that starts at the origin of the coordinate system and makes...

Homework Statement (Sin 2θ / sinθ) - (cos 2θ/ cos θ) = Sec θ just trying to match one side to the other Homework Equations all trig identities The Attempt at a Solution broke down sin2θ into 2sinθ cosθ then reduced the sinθ in the denominator giving me sinθ cosθ -...

Homework Statement \int\frac{2x}{x^{2}+6x+13}dx Homework Equations \int\frac{1}{u^{2}+a^{2}}du = \frac{1}{a}arctan(\frac{u}{a}+c \int\frac{du}{u}=ln(u) + c The Attempt at a Solution u=x+3 2xdu=2x dx x=u-3 \int\frac{2x}{u^{2}+a^{2}}du =\int\frac{2u-6}{u^{2}+a^{2}}du...

Homework Statement Solve (1+cosx)sin^2x = x^2 + 1/(x^2) Homework Equations The Attempt at a Solution RHS is always greater than or equal to 2 LHS is always less than or equal to 2 as 1+cosx is always less than or equal to 2 and sin^2x is always less than or equal to 1 so...

Homework Statement The general solution of sinx.siny=1 is 1.x=n(pi)+(pi/2)(-1)^n+1 y=m(pi)+(pi/2)(-1)^m+1 2.x=(4n+1)(pi/2) y=(4m+1)(pi/2) 3.x=(4n-1)(pi/2) y=(4m-1)(pi/2) where n,m belong to I Homework Equations Answer- 2 and 3 The Attempt at a Solution This is...

Homework Statement Hey guys, having a trig brain fart here, can you point me in the direction of simplifying: \frac{6cos\vartheta}{2sin\vartheta-3cos\vartheta} or is it as simplified as it gets? \ Homework Equations Thought about using double angle formula The Attempt at a...

Homework Statement Is there a way to determine the period of a function like f(x) = a*sin(b*x)^2 + c*cos(d*x)^2 + e*sin(f*x) + g*cos(h*x)? Homework Equations The Attempt at a Solution I know how to find the periods of sines, cosines, and arbitrary sums of the two, but the...

hi every one, i have one doubt i studied abt trignomentry. there finding the triangle angle or side of the triangle using sine function. if we are taking right angle triangle sine A = opp/hypo, cos A = adj/hypo and tan A=opp/adj. here we are finding angle for A only why we are having three...

Homework Statement Prove (using the left side): sinΘ tanΘ = cosΘ sec^2Θ - cosΘ Homework Equations The Attempt at a Solution

I received the following email: I can't see the logic in assuming (for example) that a function containing sqrt (a^2 - x^2) in the integrand would lead you to substitute x with a trig reference. Why a trig reference? What connection does the integrand, trig-less function have to trigonometry...

I'm stuck on a question from my calculus homework...T_T Here's the question... There is a large clock at the front of the lounge on the paddle steamer. The hour hand is 28 cm long and takes 12 hours to rotate once. At 2 o'clock the tip of the hour hand is 195 cm above the floor. There's...

Homework Statement So, for absolutely no good reason I decided to practice trigonometric substitution. I started with \int \left(1-x^2\right)^{-1/2} dx, and that was easy, everything canceled out nicely. Then I tried \int \left(1+x^2\right)^{-1/2} dx, and although the integral was fine...

Given sinθ = 0.6, calculate tanθ without using the inverse sine function, but instead by using one or more trigonometric identities. You will find two possible values. I found one of the values using sin^2 (theta) + cos^2 (theta) = 1 I tried using cos (90 + theta)= sin theta to find the...

Homework Statement ∫dθ/(1+βcosθ)^2 ; -1<β<1 θ=0 to 2pi Homework Equations The Attempt at a Solution attempt solution: 1) make substitution: dθ=dz/iz Z=e^iθ cosθ=1/2(Z+1/z) 2) substitute: 1/i*dz/(β+Z(1+(β^2)/2)+((3βZ^2)/2)+((β^2)Z^3)/4)+((β^2))/4Z) 3) Next ...

Homework Statement integral 31(cos^2x)(sin(2x)dx Homework Equations The Attempt at a Solution I am so lost on this problem... Any suggestions would be great