Trigonometric Definition and 1000 Threads

Homework Statement ∫ (x+2)dx/√(4x-x2) Homework Equations why was the -2 in -2(x-2) was ignored? The Attempt at a Solution so first i let u= 4x-x2 then, du=4-2x = -2(x-2) so to get (x+2) i equate it to (x-2)+4 so ... ∫ (x+2)dx/√(4x-x2) = ∫(x-2)+4dx/√(4x-x2) = ∫...

Hi, I have been representing complex numbers in graphical form in school recently. My teacher was telling me about a graph which shows all 4 quadrants and basically shows you what each quadrant is in terms of pi. Hopefully you understand what I mean, I have been looking on the internet for this...

any help with me understanding this problem would be very much appreciated. Homework Statement show, ^{π/2}_{0}\int cos^{5}xdx = 8/15 hence show ^{π/2}_{0}\int sin^{5}xdx = ^{π/2}_{0}\int cos^{5}xdx where, cos^{5}θ = \frac{cos5θ + 5cos3θ + 10cosθ}{16} sin^{5}θ = \frac{sin5θ -...

Homework Statement Finding the time derivative of sin^2( \alpha ), knowing that \dot \alpha ≠ 0 Homework Equations i know that \frac {d}{dt} sin ( \alpha ) = \dot \alpha cos ( \alpha) The Attempt at a Solution That should give \dot \alpha ^2 cos^2( \alpha ) But it's...

Homework Statement 2 ∫ dx / (x+1)√[2x(x+2)] 1 Homework Equations Let x = tan θ if √(a^2 + x^2) Where a = constant The Attempt at a Solution 2 ∫ dx / (x+1)√(2x)√(x+2) 1 2 1/√2 ( ∫ dx / (√x)(x+1)[√(x+2)] 1 Now make all x...

Where would be the best place to find every trigonometric identity, from sin[2] + cos[2] = 1, to the matrix identities (and Euler's equation would be helpful, also) Also the location of mathematical analysis symbols would be helpful, also. Thank you very much in advance :)

I'm self-studying Calculus and would like to ask some doubts about the following question: Homework Statement If, in t seconds, s is the oriented distance of the particle from the origin and v is the velocity of the particle, then a differential equation for harmonic simple motion is...

Homework Statement http://img829.imageshack.us/img829/3413/daumequation13237287425.png Prove that LS=RS. Homework Equations There are no relevant equations. The Attempt at a Solution http://img829.imageshack.us/img829/3413/daumequation13237287425.png

Homework Statement Prove that sec^(2)(x/2) divided by 1 - tan^(2)(x/2) is sec x Homework Equations Trig identities. The Attempt at a Solution I used the identity: 1 + tan^2(x) = sec^2(x) I get for numerator: 1 + tan^2(x/2) I kept denominator same: 1 - tan^2(x/2) I get the...

Alright, well I am having a difficult time getting these equations to equal out! I keep hitting trouble and have hit a road block. Here is the problem... csc(x)+cot(x) = cot(x)csc(x) tan(x)+sin(x) I am just going to work on the LEFT PART of the equation. 1 + cos(x) sin(x)...

Homework Statement Write arctan8 + arctan11 as an expression containing max one term with arctan.Homework Equations tan(u+v) = \frac{tanu+tanv}{1-tanutanv} arctan(tanx) = xThe Attempt at a Solution u = arctan8, v = arctan11 tan(u+v) = \frac{tanu+tanv}{1-tanutanv} = \frac{8+11}{1-8*11} =...

Homework Statement Calculate tan(arcsin(1/7))Homework Equations arcsinv = x => sinx = v sinx = (opposite/hypotenuse) (in a right-angled triangle) tanx = (opposite/adjacent) The Attempt at a Solution Well I realize that arcsin(1/7) is an angle. Let's call it v. I also know that arcsin(1/7)...

Hi, I am given that, for π/2 < x < π, sin x = 2/√13 a) Find Cos x b) Find tan 2 x So, what I did was: I drew a triangle and found that the missing side was equal to 3. From then, I deduced that cos x was equal to 3/√13 The problem was however that the angle must lie between the...

How do you graph f'(x) when f(x)= sin(x+sin2x), 0≤x≤∏ ? If I calculate f'(x) first by the chain rule, I get f'(x)=cos(x+sin2x)(1+cos2x), where to proceed ? Thanks for any help in advance.

Hi, I am trying to figure out what the result is when adding two sinusoids of the same frequency but with different phase and amplitudes. Specifically I want to know if the result is always another sinusoid of the same frequency. For the case of the the same amplitude I have: cos(wt) +...

Homework Statement Come up with a set of equations to draw the following picture: http://img197.imageshack.us/img197/7428/equation.jpg Homework Equations The Attempt at a Solution The circle is easy. 1000 = sqrt(x^2+y^2) I can just model the equation with sines. So y_1 = 300 * Sin(pi *...

Homework Statement 1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest...

Homework Statement 2sin\Theta-\sqrt{2}=0 Homework Equations The Attempt at a Solution 2sin\Theta=\sqrt{2} \frac{2sin\Theta}{2}=\frac{\sqrt{2}}{2} So here's my problem. Should it be positive or negative? Or just positive? Since the square root of any positive number can...

Homework Statement Hi, folks I'm curious about a question I've been doing for an upcoming math assignment. I have a professor who is really bad in English and unfortunately has made me really confused with this question and I need to know if I've got the methodology right, and if I haven't...

Homework Statement Find the following limit as x tends to zero (idk how to code this stuff properly so the lim is lim as x->0) lim (sinx-tanx)/x^3 Homework Equations lim(sinx)/x = 1 lim(cosx) = 1 lim(1-cosx)/x = 0 The Attempt at a Solution attempted to multiply by...

Hi, thank you for looking. Homework Statement Solve the following complex equation and carefully plot at least 3 solutions for each. State ALL solutions to each! State exact answers! Sin(z)=√(3) The Attempt at a Solution Here is my work. I was a little confused how to tell what...

f(x)= ((cosx)^{2}+1)/e^{x}^{2} So for the limit of f(x) as x→∞ I would just input ∞ for x. I'm confused after this though, wouldn't it just be ∞/∞ = 1? the next part says show that there exists a number c ε (0,1) that f(c)=1 I don't know what this is asking for me to solve.

Homework Statement ∫ 1/(x√(25-x^2)) dx Homework Equations by trigonometic substitution I got the following equations x = 5 sin θ dx = 5 cos θ dθ √(25-x^2) = 5 cos θ θ = sin^-1 (x/5) The Attempt at a Solution I solved it and got the following (so far, it is okay with wolfram...

Homework Statement I am integrating sin(x)^3cos(x)^3, I know the technique (I hope) and I get the right equation at the end. But if I ask wolfram alpha what the integral of the equation is and enter 0 into wolfram's answer and also enter 0 into my answer, the answers come out different. If...

find the derivatives of differentiation of trigonometric functions 1. y=cos(3x^2+8x-2) 2. y=tan^3 2x 3. y=sin5x sin^5 x 4. y=Square root of 4sin^2x+9cos^2x help here please.. i can't understand trigonometric functions sorry admin or moderator, i just search the net on how...

Homework Statement How do you solve cosx=-cos2x? The Attempt at a Solution I've tried graphing it, but just wasn't able to crack the solutions Thanks for help!

Hi, I wolud like to solve the folowing equation: A*cos(B*t)+sin(B*t)*(C-t)-D=0 (t is unknown) It is urgent. Thanks in advance. Regards Mike

Homework Statement Four congruent spheres, radius length 10 cm, are placed on a horizontal table so that each touches two others and their centres form a square. A fifth congruent sphere rests on them. Find the height of the top of this fifth sphere above the table. Homework Equations Not...

Homework Statement csc(cos^-1 u) Homework Equations Fundamental identities properties The Attempt at a Solution The book is incredibly vague on how to do this. I tried multiplying csc by (cosθ/cosθ) to get cotθ*secθ. I'm not sure if this is the right thing to do, or what to do...

Homework Statement So, the question is about evaluating limit of the equations given. The right and left hand sides should be found so that we can see if the limit exists or not. I am not sure how to write this in, but basically they're like both put in a big "{" so, i'll write both with an...

Hi All, \int_{0}^{2\pi}d\varphi \int_{0}^{\pi}\sqrt{\frac{1}{1-sin^2\theta cos^2\varphi }}d\theta I tried very hard to evaluate this integral but failed. Please help me if you know how to solve it.

Hi I have a little problem with the integrals of the following functions. integral from 0to 2pi ∫sin^2(nθ+ψ)dθ=∫cos^2(nθ+ψ)dθ=pi ψ=the phase angle.They occur in the theory of vibrations. Is it appropriate to set ψ=0 Thank you

Homework Statement a. find the tangent and normal line at P (0,0) b. find when the tangent is horizontal Equation: 3x+sin3x at (0,0) The Attempt at a Solution Find the derivative- y'=3 (?) or it it 3x+cos(3x)? But from there, I don't know how to find the rate of change to create a...

More of a general inquiry.. I was given some homework to do on trigonometric substitution. It looks to me like the goal is always to get an integral of 1 by itself, then replacing theta that results from integrating with it's x equivalent? On my homework, as long as I made the right choice...

Homework Statement My book has given me this example, with a step by step, but one of the steps have left me dumbfounded, they seem to have left a huge gap in steps.. Homework Equations The Attempt at a Solution \int sin^{5}xdx \int sin^{4}x sinx dx \int (1-cos^{2}x)^{2}...

Homework Statement A skier races down an 18 degree ski slope. During a 5.0s interval, the skier accelerates at 2.5m/s squared. What are the horizontal and vertical components of the skiers acceleration during this time?Homework Equations d = ViT + 1/2aT^2 d=distance Vi=initial velocity...

Hello, I am struggling with solving trigonometric inequalities. For example, solve: cos(\frac{\pi t}{3}) < \frac{1}{2}, 0<t<50 I wonder if one of these solutions is true: 1/ \frac{\pi}{3} + k2\pi < \frac{\pi t}{3} < \frac{5\pi}{3} + k2\pi, k \in Z 2/ \frac{\pi}{3} + 6k < \frac{\pi...

Homework Statement \int_{\frac{5\pi}{6}}^{\pi}\frac{\cos^{4}x}{\sqrt{1-\sin{x}}}dx Homework Equations \cos^{2}x=\frac{1+\cos{2x}}{2} The Attempt at a Solution i used the above equation, then expanded it all out and multiplied by the denominator and hoped i would then be able to do a...

Homework Statement Determine a three-parameter solution, with trigonometric functions using collocation at x=1/4,1/2, and 3/4. Given: u=\phi_0 + c_1\phi_1 + c_2\phi_2 + c_3\phi_3 \phi_0=0, \phi_1=sin\pi x, \phi_2=sin2\pi x, \phi_3=sin3\pi x Homework Equations...

Hi, For my exams, I am provided with a list of trigonometric functions. I do know at least a good half of those I'm supposed to know but I was wondering if I could get away with *just* knowing how to use them? I know things like sin^2(x)=1 - cos^2(x) or sin(A+B) = sinAcosB + cosAsinB but...

Homework Statement Find \lim_{x \to 0}\frac{1-cosxcos2xcos3x}{1-cosx} The Attempt at a Solution Actually my book gives this continuation \lim_{x \to 0}\frac{1-cosx+cosx[1-cos2x+cos2x(1-cos3x)]}{1-cosx} but I don't know how author arrived there. Can anyone explain it to me? Thank you

Homework Statement I've been studying trig. for my Precalculus class, and I decided to give 50 problems a try, though I got stuck in two of them: Reduce the first expression to the second in each of the following: 38.) cos2x-cos4x, cos2xsin2x and 68.) sec4θ - sec2θ, sec2θtan2θ...

Homework Statement Deduce that 0 ≤ ≤ 10/9 for all values of x. Homework Equations The Attempt at a Solution Is it possible to sketch a graph for ? How? Or is there any methods to find the max./min. value of ? Please enlighten me...

Hi, I was wondering, just out of curiosity, what family of integrands can be evaluated by making a cis(x) substitution, cis(x)=cos(x)+isin(x), I can't seem to find any examples or anything at all and was wondering if someone could provide an example or inform of how to make such substitutions.

In the following question I figure that i need to prove that h holds true with the trigonometric identity subbed into the denominator. I'm not sure how to simplify the equation any further after that though. Can someone provide any insight...

Homework Statement Show that arcsin(1/sqrt(5)) + arcsine(2/sqrt(5)) = Pi/2 Homework Equations The Attempt at a Solution Can someone please give me so much as a hint?

Homework Statement prove that sin^4theta + cos^4 theta =1/4 (3+cos4theta).hence,find the greatest and least value of sin^4theta + cos^4 theta. please give hints to start . no idea at all...i start from the RHS and get 2cos^4 theta - 2 cos^2 theta +1 , then how sin^4theta + cos^4 theta...

Homework Statement Hi, I'm trying to solve this problem and guess I'm doing something wrong. Evaluate Integral tan(x)^5*sec(x)^4 dx Homework Equations integral tan(x) dx = ln(|sec(x)|) integral tan(x)^n dx = tan(x)^(n-1)/(n-1) - integral tan(x)^(n-1) dx tan(x)^2+1=sec(x)^2 The Attempt at...

Hi, I just had this idea pop into my head... Can you use a trig sub with a reference triangle who has sides equal to zero? or more like a value close to zero such as dx or da or something? For example integral 1/sqrt(9+dx^2) (dx)^2 would have a reference triangle were the hypotenuse is...

Homework Statement Use the method of trigonometric substitution to evaluate the following: \int\frac{x^{2}}{\sqrt{4-9x^{2}}} Homework Equations The only relevant equation that I could think of for this one was the trig identity: sin^{2}\vartheta + cos^{2}\vartheta = 1 The...