Trig Definition and 1000 Threads

Homework Statement Mass m sits on a frictionless, horizontal table. Assume: - All vertical forces acting on m (such as gravity and the normal force) sum to zero. - All applied forces act parallel to the table When a force of magnitude F is applied to mass m, it accelerate at magnitude a...

Homework Statement Simplify: sin^3(x) - tan^2(x) - cot^2(x) - cos^2(x) + 1 - sin(x) Homework Equations n/a The Attempt at a Solution I don't know where to go after I get to: sin(x)[sin(x) - cos^2(x)] - tan^2(x) - cot^2(x)

Homework Statement The context of the problem is that it's a vector valued function (VVF) problem where I'm supposed to sketch a curve generated by a VVF. To make the sketching easier I'm supposed to convert a VVF to a real valued function so that I can take advantage of the shape of a curve...

problem: sin(x)^2cos(x) integrate from 0 to pi/2the way I tried this is by making u = sin, and then working with du to make cos cancel out the next thing I did was check my new intervals by plugging in pi/2 and 0 into the u function (becomes 0 to 1) next, I took the anti derivative of u, which...

Homework Statement 2sin(4x)-sin(2x)-(√3)cos(2x)=0 x is [0,2π] Homework Equations The Attempt at a Solution Using trig identities: 8sinxcos3x-6sinxcosx-√3(2cos2x-1) Please help me with this problem. I have no idea where to go from here. Thanks.

Homework Statement -sin x = √3 * cos x where x is [0,2π] Homework Equations The Attempt at a Solution Would it be wrong to square both sides and then factor? sin2 x = 3cos2 x 1-cos2 x = 3cos2 x 0= 4cos2 x - 1 0 = (2cos x -1)(2cos x + 1) Now I solve the factors (2 solutions...

Would it hurt to memorize the trig ident in the paint doc? I am thinking if I do it will save me some time in the long run with integrating. Also, I know I've asked this question before but I can't seem to find my old post... can some one send me a link of important integrals to know, (not...

Homework Statement ∫sin2xcosx x=0,pi/4 Homework Equations The Attempt at a Solution By double angle magic: ∫sin2xcosx= ∫2sinxcos^2x u=cosx du=-sinxdx -2∫u^2 -2(u^3)/3 -2cos^3x/3 = -1/(3√2) for x=pi/4 How does that look folks?

Homework Statement use substitution to evaluate the integral Homework Equations 1)∫ tan(4x+2)dx 2)∫3(sin x)^-2 dx The Attempt at a Solution 1) u= 4x+2 du= 4 (1/4)∫4 tan(4x+2) dx ∫(1/4)tan(4x+2)(4dx) ∫ (1/4) tanu du (1/4)ln ltan(u)l +c 2) u=sinx du= cosx or u=x du = 1 ?

Homework Statement This is an integration of an inverse trig function. I don't see how they go from 1/2 to 1/4. I understand how they get the 1/2, du = 2dx, divide both sides by 2, but where does the 1/4 come from?

Hey everyone. Sorry to post another topic, but i thought this would be easy to find on google, to help me with , but i can't find it. All I am really lookin for is someone to let me know if my answers are right, and if not, then how i can fix them :) Anyways, i was asked to graph...

Homework Statement \int\frac{\sqrt{16+x^{2}}}{x} Homework Equations The Attempt at a Solution set x=4tant dx=4sec^{2}t dt so after plugging in and using a quick trig identity I get: \int\frac{16(sec^{2}t)*4sec^{2}t dt}{4tant} Then after a quick cleanup: 16*\int...

Before taking Differential Equations/Linear Algebra in my first year of college, I am brushing up on Algebra I/II, Pre-Calculus, and Calculus I/II. Should I also run through Trigonometry as well or should I not waste my time on it if I don't have enough time to go through everything else first...

Homework Statement 1. Simplify: [sin(x-pi) / cos(pi - x)] - [tan(x-3pi/2) / -tan(pi + x) 2. Solve: 1 - tan(2x + pi/2) = 0, 0 ≤ x ≤ 2pi Homework Equations cos(x - y) = cosxcosy + sinxsiny sin(x - y) = sinxcosy + cosxsiny tan(x + y) = tanx + tany / 1-tanxtany tan (x - y)...

Homework Statement \int\stackrel{tan(8)}{tan(1)}\frac{dx}{x^{2}+1} Homework Equations The Attempt at a Solution \int\stackrel{tan(8)}{tan(1)}\frac{dx}{x^{2}+1}tan^{-1}x|\stackrel{tan(8)}{tan(1)}tan^{-1}(tan(8))-tan^{-1}(tan(1))8-1=7I'm fine with this, but my instructor said "Hint: The answer...

Homework Statement A pole of length L is carried horizontally around a corner where a 3-ft wide hallway meets a 4-ft wide hallway. For 0 < \theta < \frac{\pi}{2}, find the relationship between L and \theta at the moment when the pole simultaneously touches both walls and the corner P...

Homework Statement find the derivative of the function f(x)=arcsec(4x) Homework Equations I think this is a Relevant equations. d/dx[arcsecu]=u'/(|u|(√u2-1) The Attempt at a Solution f'(x)=4/(|4|(√42-1) =1/√15 I keep getting wrong in my online homework why? :confused:

Homework Statement It has been a while since I have really been involved in trig seriously, But I felt it appropriate to go in this particular forum because in my classes from years back "precal" was the title associated with trig (: The Problem: sin(X) / sin(X/2)...

Homework Statement For the function f(x) = 3sin 2x, find the instantaneous rate of change at point A (\frac{\pi}{6}, f(\frac{\pi}{6})) Homework Equations iroc = instantaneous rate of change iroc= \lim_{h\to 0} \frac{f(a+h) - f(a)}{h} The Attempt at a Solution iroc = instantaneous...

Homework Statement I got to a place in a problem where I need to do a sticky integral, and I'm hoping I can use a trig substitution. If not, I will need to solve the main problem another way :( \int_0^\infty \sqrt{1+(e^{-\theta })^2} \; \mathrm{d} \theta Homework Equations 1+\tan ^2...

Homework Statement Solve the equation 5sin2x-3=0, given values of x in the interval -180≤x≤180 correct to 1 decimal place. Homework Equations for sin: take inverse 180-θ ±360 The Attempt at a Solution I rearranged the equation to sin2=3/5 but I am not quite sure what to do...

Homework Statement sinx=-1/2 how do I find x without using a calculator? Homework Equations The Attempt at a Solution I really don't have any idea.

Homework Statement The diagram below shows two pith balls, equally charged and each with a mass of 1.5 g. While one ball is suspended by a thread, the other is brought close to it and a state of equi- librium is reached. In that situation, the two balls are separated by 2.6 cm and the thread...

Homework Statement Simplify this expression: csc(x)sqrt(sec^2(x)-1) with 0 less than or equal x less than pi/2. Homework Equations The Attempt at a Solution Not really sure what they want here, but would a good place to start be to square the entire expression to get rid of the...

Trig identity with natural logs and absolute value?? Homework Statement -ln|csc(x) + cot(x)|= ln|cscx(x)-cot(x)| Homework Equations The Attempt at a Solution I got that csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x), giving me a common denominator, added together I have...

Homework Statement Question paper: http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202011%20-%20QP/6665_01_que_20110124.pdf Mark scheme: http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202011%20-%20MS/6665-01-msc-20110223.pdf...

Any/All help is appreciated :) Thanks! Homework Statement All that has to be done is proving that these two sides are equal. Basically, you just work through the problem until both sides are the same. (csc(x)-sec(x))/(csc(x)+sec(x)) = (tan(x)-1)/(tan(x)+1) Homework Equations...

Hard Grade 12 Trig. Questions :( Homework Statement http://img831.imageshack.us/img831/8389/daumequation13263429629.png Homework Equations No equations are required. The Attempt at a Solution http://img845.imageshack.us/img845/9519/34851996.png...

Homework Statement http://i1094.photobucket.com/albums/i451/LearningMath/vectorconfusion.png Question 1: Is this mainly saying that when the angle is greater than 90 degrees use the reference angle to evaluate a trig function? Question 2: Is this then saying that if you choose to...

Homework Statement My problem is as follows: find the inverse of 3x+1+\sin(x) with the domain [-\frac{\pi}{2},\frac{\pi}{2}] Homework Equations The Attempt at a Solution for this would I just try to solve as normal by setting y=f(x) then using the fact that \arcsin(x) = y or is...

Homework Statement Solve the equation 2 - cos2x =sinx. Give the solution in the interval 0≤x≤360. Homework Equations sin2x+cos2x=1 I know for sin you take inverse. Then subtract that from 180. I believe those are basic angle then you +/- 360. ? The Attempt at a Solution I tried...

Homework Statement Now this is a problem that my sister had on her Calculus homework, and I can't seem to figure it out. I believe a similar triangles argument is necessary, but I'm not sure, and trig always was my weak spot. The problem is as follows: Homework Equations The Attempt at a...

Since I am new to PF (hi!), before I go any further, I would like to a) briefly note that this is an independent study question, and that its scope goes beyond that of a textbook question - i.e., I believe that this thread belongs here - and b) also note that I am new to analysis and early...

Homework Statement g(x)=x - sin (pi*x) at [0,2] Homework Equations all values where g'(x)= 0 (or non-existant) are critical points The Attempt at a Solution g'(x)=1 - ╥(cos(╥X)) 1/╥=cos(╥X) cos^(-1) (1/╥) = ╥X X=(cos^(-1) (1/╥))/╥ x=.397 and x=? 2nd point

I have these practice trig problems for a test. I understand the simple graphs but its these more complicated ones. y=2sec(3x-pi) my approach: I first find the period and phase shift. Since the period of a normal secant function which is 2pi. Then the period of this one is 2pi/3. The...

Please, check my work. Homework Statement a) Show that sqrt{[1+tan^2x]/[1+cot^2x]}=tanx b) Show that [cosx+sinx]/[cosx-sinx]=1+[2tanx]/[1- tanx] c)Show that cotxcosx+tanxsinx=(cosecx+ secx)(1-sinxcosx) d) Show that cosec^2x-cosecx=cot^2x/[1+sinx] e) Show that sin^3x-cos^3x=...

My homework is to find the sin or cos value of angle that is not directly known on the unit circle. So of course we are given an equation which adds or subracts known values to get the desired one. The problem is that I don't think memorizing them is helping me learn. I want to know how the...

Hey everyone, new member here with a quick question, but first some background. I'm 20, and cannot afford college right now unfortunately, I am however about to start a truck driving job in Texas where I will have 12 hours a day of off time, doing nothing nothing, save my needed sleep, I...

The problem is as follows: A mass is held by two cables attached to a wall and ceiling. The mass M is 5 kg and the angle between the string and the vertical is θ= 25° a) Determine the tension in the cable attached to the ceiling. I know that the answer is 55 N (because she posted the...

Homework Statement Solve the equation: sin(x+∏/6)=2cosx for 0≤x≤2∏ Homework Equations sinAcosB+cosAsinB The Attempt at a Solution sin(x+∏/6)=2cosx 2cosx=(√3)/2sinx+1/2cosx How do I solve from here?

Homework Statement Solve the equation cos(x-60)=sinx Homework Equations cosAcosB+sinAsinB The Attempt at a Solution cos(x-60)=sinx cosxcos60+sinxsin60=sinx 1/2cosx+(√3)/2sinx=sinx How do I then solve to find x for0<x<360

Homework Statement I am trying to find the limit of the following question: lim (as x approaches infinite) sin[ arctan(((x^3)+2)/((x^2)+5)) + (((cosx)^2)/((|x|)^(1/2)))*arctan(2x)] (to see the above function better, without a million brackets, please use the following link)...

I'm having troubles solving this integral. ∫ (sinx)^2 / √( a - b*cos(x)) dx ; a & b just constants I've tried many routes but get stuck. And when substitution and product rule methods seem to fail. Are there other methods useful to go to when integrating strange functions?

Homework Statement evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3 Homework Equations The Attempt at a Solution the answer in the textbook is 8/27 i figured they got that by raising 2 to the 3rd and 3 to the 3rd but I'm not entirely sure what happens to the...

Homework Statement how is the differential of 1+tan2(4x) 8*tan(4x)*sec2(4x) Homework Equations The Attempt at a Solution So 1 differentiates to 0 (we can now ignore this) tan2(4x) differentiates to 2*tan(4x)*sec2(4x)? BRING POWER FORWARD, DOWN POWER BY 1, DIFFERENTIATE TERM IN BRACKET by...

TI-84 HELP! The formulas under the CONICS app keeps converting into trig... It saying a circle is x=rcos(T) + H instead of (x-h)^2 + (y-k)^2 = r^2 How do I get the 'normal' formulas back? PLEASE HELP!

Homework Statement lim(x -->0) (1-cos(14x))/(xsin(18x)) Homework Equations None? The Attempt at a Solution The hint tells me to use L'hopital's rule through which I got lim(x-->0) (sin(14x))/(18xcos(18x)+sin(18x)) (I factored out the 14 in the numerator) That gave me a 0/0 so I did...

Question: Find the area under the graph y = cos(x) from x = 0 to x = pi/2 Solution: A = Lim ( ∏/(2n) * Ʃ cos( ∏i/(2n)) = ? Start: i = 0 and End: n = n n → ∞ Just like there is a theorem for adding consecutive numbers... n(n + 1)/2.. Is there one for trig functions?

Homework Statement Alright, so I am going through the solutions to one problem that has me stumped, and initial instinct tells me it is wrong, however, I figured I would get clarification. The Attempt at a Solution sin(2t)=cos(2t) tan(2t)=1 2t=\pi{/}4, 5\pi{/}4 However, the book...

Hello all, I'm wanting to learn how to derive all of the trig identities (well, not all, but the most common) rather than memorizing them. Perhaps someone here could provide me with a list of "essentials" that are the framework for deriving others. For example, I know there are a few that can...