Trig Definition and 1000 Threads

Hi I am in need of some help for this question: 1+tanx/1-tanx = tan(x+(∏/4)) It is easy to solve with the tan trig identites on the right side however, my teacher had told me to do it with SIN and COS only. I am not sure if its possible and was looking for some insight Left Side...

I used Wolfram Alpha to evaluate: lim tan[(2nπ)/(1 + 8n)] n->infinity it says that it can use the continuity of tan(n) at n = π / 4 to rewrite the aforementioned function as: tan[lim ((2nπ)/(1 + 8n))] n->infinity What is it talking about? I was taught to use certain properties of trig...

trig functions cross multiplying?? Homework Statement sinx/cosx - 2sinxcosx/1Homework Equations none??The Attempt at a Solution when I cross multiply, should it be sinx-2sinxcosx/cosx or sinx-2sinxcos^2x/cosx ?? here's a pic: http://tinypic.com/r/24fgvmv/6

Homework Statement Homework Equations The Attempt at a Solution I can solve the first part of the question. -2 ≤ k ≤ 2 because -1 ≤ sin(x) ≤ 1. How do I solve the second part of the question? Thanks.

Homework Statement I'm stuck at an attempt to solve an integration step. I think I'm supposed to trig substitute? Homework Equations http://img685.imageshack.us/img685/9158/unavngivetn.png It is the second to third equation I'm having a hard time with The Attempt at a Solution From second...

I am trying to integrate -tan(x)sec^2(x) and getting -tan^2(x) / 2. When I put it in wolfram alpha it gets the same answer when I press show solution, but without pressing it it shows -sec(x)/2. So I am wondering, is it the case tan^2(x) = sec(x)?? I don't remember this as a correct trig...

prove that cos\frac{\pi}{12} = m and sin\frac{\pi}{12} = n, where m = \frac{\sqrt{3} + 1}{2\sqrt{2}} and n = \frac{\sqrt{3} -1}{2\sqrt{2}} could anyone give me a start on how to do this?

when I differentiate: $$ln4x+sin(x)$$ I get: $$\frac{1}{x}+cos(x)$$ and Wolfgram agrees But then when i test this by calculating indefinite integral, I get: $$ln(x)+cos(x)$$ Which leaves me with three questions: 1. what happened to the 4? 2. why isn't it integrating back to (at least)...

Homework Statement Integral of ... h(x) = x^5 + x^5 + [cos(x)]^6 Homework Equations The Attempt at a Solution so it would be 1/6x^6 + 1/6x^6 + 1/7[sin(x)]^7 is this correct?

Homework Statement If theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per measure at the instant when x equals 3 units? The Attempt at a Solution I drew the triangle and I came to the conclusion that I needed to use 5sin(theta)=x...

Homework Statement cos(theta) = -3/4, pi <= theta <= 2pi Homework Equations The Attempt at a Solution I forgot how to do this. How do I use the special triangles to do this question? Do I need to square the sqrt(3) / 2 one or something? Thanks.

Homework Statement Find the derivative of y = sin(πx)2 Homework Equations Chain Rule: y' = f'(u) * u' The Attempt at a Solution (See attached image) The answer according to the textbook is 2π2xcos(πx)2. What am I doing wrong here?

I am studying trig on my own in order to prepare myself for calculus. Just wondering how much I need to know. For example, would being familiar with the unit circle and inverse functions suffice, or should I thoroughly study every chapter of my trig book and know every concept to the best of my...

In class my teacher said in general if you have a equation such as sinαcosα = cosα you shouldn't divide through by cosα as cosα can be 0 and dividing by 0 Is undefined, instead we should factorise, which makes sense. However I was going through a question which gave sin2α = cos2α and in the...

I am currently working a physics problem and I have run into some math that I don't understand. y = 4.0m + 4.0m(sin theta) = 4.0m(1+sin(theta)) In the problem I am trying to find a specific height at a certain angle (pendulum problem). I have found some help online that walks me through...

(sin^3(x)-cos^3(x))/(sinx-cosx) = 1+(sinx*cosx) I'm following a path similar to the post on http://www.askmehelpdesk.com/mathematics/verify-identity-sin-3-x-cos-3-x-sin-x-cos-x-1-sin-x-cos-x-500483.html However, I keep getting 1-(sinx*cosx) when solving for mine as I end up with...

Hi, I have the answers to the following question, but i do not know how to calculate them from the first: Find all the solutions to the following equation Sin( (5x)/2 + 15°) = 0.34 Where 0°≤x≥360° The answers are...

Homework Statement \intsin^{5}x cos x dx Homework Equations sin^{2}x + cos^{2} x = 1 The Attempt at a Solution I've at least written down that sin^{5}x = (sin^{2}x)^{2} sin x. Then I set sin^{2}x equal to 1 - cos^{2}x. I then did a u-substitution, setting u equal to cos x to...

Homework Statement From introduction to analysis,by Arthur P. Mattuck,problem 20-1. Problems 20-1 One way of rigorously defining the trigonometric functions is to start with the definition of the arctangent function. (This is the route used for example in the classic text Pure Mathematics by...

Homework Statement Ok, you can see the question and how far I got from the image. Lim x--> infinity So, let's take the LEFT side: how does 3x-1 / x turn into just 3? I know the answer is 3, but from where you can see in the pic, that is where I get stuck, and don't know how to go on...

I'm having trouble understanding a trig identity and only include it here (rather than in trig forum) as it touches on a -broader- derivative problem. Here it is: $$\frac{d}{dx} \ e^{sin^2(x)}=e^{sin^2(x)}\cdot 2sin(x)cos(x)$$ $$=e^{sin^2(x)}\cdot \ sin(2x)$$ I have attached a proof of the...

If I have a right triangle and I know the hyp and the length of the opposite side of the angle I want then how do I find that angle? For instance: hyp = .9m and side opposite the angle I want = 1.5m. I tried dividing 1.5/.9 = 1.7 then I thought all i had to do was take the inverse sin of 1.7 and...

Apparently our professor expects us to know these half-angle identities (http://www.purplemath.com/modules/idents.htm) Without going through them in class or us learning them in high school.. Can somebody explain how these were derived? Does the derivation come from the angle-sum and...

Homework Statement Find the determinant of the matrix {{cos 25°, sin° 65}, {sin 120°, cos 390°}} (sorry, can't latex). {cos 25°, sin° 65} is first row and {sin 120°, cos 390°} is the second one. Homework Equations cos(a + b) = (cos a)(cos b) - (sin a) (sin b) The Attempt at a...

Homework Statement Hi everyone. I understand the basics of trig graphing; but am having a hard time understanding f(x) first of all what to f and x stand for? Above and beyond that any help understanding f(x) or a link to a website that might help me would be great. Homework Equations...

Hello, I am working through some very old (1980's) computer code and need to understand how a particular derivative was calculated. Can someone explain to me how it is that if: \vec{a}=\vec{f}\times\vec{g} \vec{b}=\vec{h}\times\vec{g} and...

Homework Statement I need to prove both of these (in exercise 11) http://postimage.org/image/x7shxv11f/ Homework Equations The dot product The Attempt at a Solution

now say we have cos^2(3t), how would you go about computing it with the 3t? i can manage cos^2(t) but I'm not sure how to take it that one step further in the link below is what I've managed so far.. [SIZE="5"]SOLVEDI worked it out. If anyone's interested in the future, Just start it off as...

I am having trouble figuring out these two word problems. I have attached drawing on how I have set them up the diagrams up, but I seem to be going wrong on both. Here are the two questions. 1. A rocket lifts off vertically and travels to height of 5000m. The second stage cuts in and takes the...

Hi everyone, a classmate and I are studying for a test and have been trying to work out the following problem for the past hour and a half with absolutely no progress. Please point us in the right direction :) Homework Statement Someone at a third floor window (12m above ground) hurls a ball...

π/3 ∫tan^5 x sec x 0 I want to split the tan^5 x into a (sec^2 x - 1) but I only have sec x. So I'm a bit stuck. Help is appreciated.

Homework Statement You know the U substitution proofs for inverse trig functions that go like this: \int\frac{1}{a^{2}+x^{2}}dx \int\frac{a\frac{1}{a}}{a(1+\frac{x^2}{a^2})}dx let u = x/a du= dx/a ... \frac{1}{a}tan^{-1}(x/a)+cI have searched google and can't find any of these proofs for...

Homework Statement I am reviewing some trig, and I forgot how to do this. Please let me figure this one simple thing out. Here is the questions. Find the exact trig ratios of 5∏/6 Ok, now look at my diagram below to see where I am having trouble with! What simple process am...

Homework Statement Please help me understand the reason for substituting various trig identities into trig functions with powers instead of integration by parts. Does integration by parts not work on trig functions with powers, or is it just so much work that substituting trig identities to...

Homework Statement I have a graph with the functions f(x)=sin2x and g(x)=cosx. The 2 graphs intersect at point B. They want me to find the co-ordinates of B. Homework Equations The Attempt at a Solution Must I equate the two graphs? sin2x = cosx 2x = 90-x, 3x = 90, x=30...

Homework Statement cos(-225) The Attempt at a Solution Would it become, -cos45 ? Just want to make sure.

Homework Statement I am trying to work through a trig review I found online, but this is the type of question I am needing to be able to solve. If anyone can be so kind to send me a link to a tutorial on how to solve these, I would REALLY appreciate it. Anyways, on to the question! :)...

The integral from 0 to pi/2 of: cos(t)/sqrt(1+sin^2(t)) dt I'm supposed to use trig. substitution to find the solution. I started by using the formula a^2+x^2 to get x=atanx. In this case, sin(t)=(1)tan(θ), and so cos(t)dt=sec^2(θ)dθ and so I substituted this into the equation and got...

Hello, I have the following problem part (b) which I already solved as you can see in the attached image. So I am not asking homework questions, I merely reviewing my homework for a better understanding for the test. I obtained the answer from a friend showing me his method. However, I am...

Homework Statement [SIZE="4"]\int\frac{1}{\sqrt{16-x^2}}dx Homework Equations [SIZE="3"]csc\theta=\frac{4}{\sqrt{16-x^2}} [SIZE="3"]4cos\theta=x [SIZE="3"]-4sin\theta d\theta=dx [SIZE="3"]\theta=arccos(\frac{x}{4}) The Attempt at a Solution Using these facts, I concluded...

I feel kind of dumb asking this (it's been a while sense I took precalc) but I always thought that if I had something like arctan(stuff) = answer that if I added any whole integer multiple of 2pi to the answer I would get equivalent answers. Is this correct? Like answer - 4pi = answer...

I'm solving some trig functions and ran into a notation that says Sin(90°-θ) What does it mean? I know what Sin θ is and I know that Sin 90° = 1.

I am given two sides of a triangle and the angle in/between them: 9 in/s and 4.5 in/s at 50 degrees. I am using the Law of cosines to get the third side which is 7.013 in/s. I then used the law of sine to find the two remaining angles. I have continually gotten 79.4 for one angle and 29.4...

Homework Statement ∫(4x^3)/√(x^2+4)dx Homework Equations The Attempt at a Solution So, I let x= 2tanθ dx= 2sec^2θ dθ So, √(4tan^2(θ)+4)=2secθ ∫(4x^3)/√(x^2+4)dx=∫((32tan^3(θ))/(2secθ))2sec^2(θ)dθ. Would it go to ∫16tan^3(θ)2sec(θ)dθ or ∫32tan^3(θ)sec(θ)dθ

[FONT=arial]After a long summer, I finding my new C3 homework a bit tricky, so any help would be great! Here is the question: sec(θ-150 degrees)=4 (solving for theta is greater than or equal to -180, but less than or equal to 180) So I know that sec is the reciprocal of cos so I changed the...

Homework Statement Define functions f and g on [-1,1] by f(x) = xcos(1/x) if x≠0 and 0 if x = 0 g(x)= cos(1/x) if x≠0 and 0 if x = 0 (These are piecewise defined. I don't know how to type them in here.) Prove that f is continuous at 0 and that g is not continuous at 0. Explain why...

Homework Statement The definite integral of ∫(x^2 √(a^2-x^2) dx from 0 to a Homework Equations The Attempt at a Solution So i don't need actual help with this problem. I got the answer, (π*a^4)/16 and I verified with the back of the book. The question I have is whether this...

Here is my problem: cot(arcsin(x)) my awnser: cot= x/(1-x)^1/2 The online program were suppose to use says I am wrong but I am not sure what I did wrong.

Evaluate the integral \int \frac{x}{(x^2 - 4) \sqrt{x^4 - 8x^2}} \, dx by making the substitution u = x^{2}Homework EquationsThe Attempt at a Solutionu = x^{2} - 4 so \frac{du}{2}= xdx \int \frac{1}{(x^2 - 4) \sqrt{x^4 - 8x^2}} \, xdx \frac{1}{2} \int \frac{1}{(u) \sqrt{x^4 - 8x^2}} \...

Homework Statement A block with mass M is held statically on an overhang by a force Mg applied horizontally and the force of friction on the overhang. What are the normal and frictional forces? For what angles θ does the block remain at rest? The Attempt at a Solution In the picture...