What is Trig: Definition and 1000 Discussions

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...

Homework Statement ∫5/(4x√(9-16x2)dx Homework Equations I am pretty sure this is in the form of ∫du/(u√(a2-u2) The Attempt at a Solution setting u=4x a=3 and du=4dx so 1/4du=dx I get: -5/12 sech-1(4x/3) + C Is this right or am I using the wrong definition? Just trying to...

Homework Statement Find constants a, b and c such that sin(∅)^5=asin∅+bsin3∅+csin5∅ Homework Equations The Attempt at a Solution I expressed sin in its complex form (if that's what its called) and put it to the power 5, and then multiplied each bracket out one at a time, and...

Homework Statement Solve each equation for 0≤\Theta≤2\pi (exact values where possible) The question: 2cos^22\Theta - cos2\Theta - 1=0 Homework Equations cos2\Theta = 2cos^2\Theta-1 The Attempt at a Solution 2cos^22\Theta - 2cos^2\Theta - 1 - 1 = 0 2cos^22\Theta - 2cos^2\Theta - 2 = 0...

A field goal kicker kicks the football so that it leaves the ground with velocity V that is 50 degrees above horizontal. The ball travels for 3.24s and hits the crossbar 10.00 ft above the ground. Neglect air resistance. Find the velocity after the kicker kicks the ball. Find the horizontal...

2 Questions here! (I'm not exactly sure if it's allowed, but I want to avoid posting too many threads) Homework Statement 1)Find the following definite integrals by using a trigonometric substitution: d)1/2∫1dx/(√(2x-x2) Homework Equations x=asinu The Attempt at a Solution From...

Homework Statement What values of X between 0 and 2 pie radians satisfy each of the following: 1. |sinX|<0.5 2. |cosX|>0.5 Homework Equations The Attempt at a Solution Well the values of X lie between 1. -0.5 < sinX <0.5 2. cosX< -0.5 and cosX>0.5 How do you find the...

Homework Statement I am working through a calc 2 problem. I managed to get here without really completely understanding trig. There was a point in the problem where θ=Tan-1(-2/2) = -Pi/4. How does this work? Homework Equations I do not know any relevant equations The Attempt at a...

Homework Statement cos^2x+2sin^2x=-1 Solve for x Homework Equations The Attempt at a Solution I don't really know how to start. I know cos^2x+sin^2x=1 but I don't think I can apply that with the 2 thrown in there.

[b]1. An observer is next to a river and wants to calculate the distance across the river. He measures the angle between his observations of two points on the shore, one on his side and one on the other side, the angle coming out to be 28º. The distance between him and the point that is on the...

Homework Statement I'm trying to solve this DE: 4xy''+2y'+(cosx)y=0 using a series solution. Homework Equations The Attempt at a Solution See attached PDF. I tried writing the cosine term as an infinite series, but that gives me a messy double summation. And in the end, I get an...

Homework Statement ∫[sin4(t)cos2(t) + cos4(t)sin2(t)]dt The Attempt at a Solution Is there any way to do this integral using a substitution, or do I need to just split it into two integrals and apply a very messy series of half-angle identities? Thanks.

Homework Statement find dy/dx Homework Equations x+tanxy=0 The Attempt at a Solution d/dy(x+tanxy) x+sec^2(xy)((1)(dy/dx))+(1)(tanxy)=0 dy/dx(sec^2(xy)+x+tanxy=0 -x-tanxy -x-tanxy dy/dx(sec^2(xy)/(sec^2(xy)=(-x-tanxy)/(sec^2(xy))...

Homework Statement find dy/dx Homework Equations x= tan y The Attempt at a Solution d/dx(x=tanY) 1=(tan(dy/dx))+sec^2+y

Homework Statement Find the 73rd derivative of f(x) = sin(2x) + 3 (Hint: Take the first five derivatives to find a pattern) Homework Equations dy/dx The Attempt at a Solution I took the first five derivatives to find the pattern: dy/dx = 2cos2x d2y/dx2 = -4sin2x d3y/dx3 =...

Homework Statement ∫(dx/((1+x^2)^2) from 0 to ∞ Determine whether the improper integral converges and if so, evaluate it.Homework Equations 1+ tan^2(x) = sec^2(x) 1/sec(x) = cos(x) The Attempt at a Solution Initially I had no idea how to approach this problem. The answer in the back of the...

Homework Statement lim x->0 (2x+1-cosx)/(4x)Homework Equations The Attempt at a Solution factor out 1/4. get stuck because of cosx.. and I'm not using l'hopital even though I know it.

Homework Statement There are four pieces of rope tied between four trees. Given the forces of tension in three of the strands, find the force of tension in the remaining rope. Rope 1: 2.1x10^-3N [20°E of N] Rope 2: 1.6x10^-3N [60° E of S] Rope 3: 1.9x10^-3N [40° W of S] Homework...

Homework Statement Here is a link to the project: http://www.stewartcalculus.com/data/ESSENTIAL%20CALCULUS%20Early%20Transcendentals/upfiles/projects/ecet_wp_0504b_stu.pdf" I'm on #1 and and I am at a loss to figure out what they are looking for. This sentence is really giving me...

Homework Statement I missed one class on trigonometric identities in integrals, and I feel that one is needed here: \int^3_0\frac{1+arctan(\frac{x}{3})}{9+x^2}dxHomework Equations The Attempt at a Solution Again, I'm unsure what to do. I think that it is a trig identity, but I could be wrong...

Homework Statement Find the derivative: y=sec-1(1/2t3) Homework Equations \frac{\frac{du}{dx}}{|u|\sqrt{u^2-1}} The Attempt at a Solution I have an example to follow, but I don't know how step 1. became step 2.?...or more exactly the last part under the radical? (1-4t^6) instead...

Homework Statement Find the limit as x approaches ∏/8, (cos(2x)-√(2))/(x-∏/8)Homework Equations cos(2x)+cos(2a)The Attempt at a Solution I tried to multiply the conjugate of the terms but ended up stuck there, don't know how to go on. Please help.

Homework Statement Rewrite sin^4 xtan^4 x in terms of the 1st power of the cosine. Homework Equations sin^2 x=(1-cosx)/2 tan^2 x=(1-cosx)/(1+cosx) The Attempt at a Solution For this problem, I tried to rewrite tan^2 x as (sin^2 x/cos^2 x) But then I ended up with a...cubic...

Homework Statement 1. sin(1/x) as x->infinity 2. tan(7x)/sin(5x) as x->0 3. General question--when finding the derivative (through implicit diff.), and I have something like y=(5x^2)y, what parts am I supposed to use the chain rule, and when am I supposed to use the product rule? The...

Homework Statement \lim_{x\to\0} \frac{2tan^2x}{x} The Attempt at a Solution \lim_{x\to\0} \frac{2tan^2x}{x} \\ = \frac{2 tanx tanx}{x} \\ = \cfrac{2 \cfrac {sin}{cos} \cfrac {sin}{cos} ? Edit: Oh boy none of my latex is working. :( Homework Statement lim x--> 0 (2tan^2x)/xThe Attempt at...

Find dy/dx of these functions: 1. y=sin-1(1/3x) dy/dx=1/(√1-(1/3x)2 (1/3) dy/dx=1/(3√1-(1/9x2) However the book answer is 1/√9-x2). How did they get this? 2. y=sin-1(1/x) dy/dx=1/√1-(1/x)2 (-1/x2) If i tried to simplified it by multiply it by x^2/x^2then dy/dx= -x^2/x4√x2-1 which...

Homework Statement Establish the identity: 1+cos(2θ)+cos(4θ)+cos(6θ)=4cosθcos(2θ)cos(3θ) Homework Equations cos(a)+cos(b)=2cos((a+b)/2)cos((a-b)/2) The Attempt at a Solution I understand how to do a simple cos(+/-)cos problem according to the Sums as Products equations, but I am...

Homework Statement cos^-1(sin(5pi/4)) Homework Equations n/a The Attempt at a Solution I began by finding the reference angle of 5pi/4 by subtracting pi, and I got pi/4. pi/4 must be part of an isosceles right triangle, so I drew a diagram with sides 1,1, and √2. I found sin pi/4...

Hi guys. I was trying to play with trig function and I finally ended up with this equation: \sqrt{2}sin(\frac{\pi}{2}-d\theta)=1-dx How can I determine a function \Theta(x) from that equation? Please, can anyone help me?

I have spent over an hour trying to solve this equation but I cannot seem to do anything with the equation after I get to the point where .529cosx + 0.916sinx = 1 I've tried doing a million other substitutions and methods but I just don't know how I should go about finding x. Any...

So basically I know what the answer is to the problem and the steps on how to get there, but during the steps I'm not sure why one thing happens. sec(7pi/6) =1/(cos7pi/6) =1/(-cos(pi/6)/ <--- I'm not sure why the 7 disappears in this step and the cos becomes negative. I get the feeling...

Homework Statement Homework Equations How did they come up with \frac{1}{2}+k for the equation of the vertical asymptote? I understand everything else except this.The Attempt at a Solution On this particular exercise, I graphed it and saw that each of my vertical dashed lines were all one whole...

Homework Statement cot^2(Cos\theta)Homework Equations chain rule f prime (x) = f prime(g(x) * g prime (x) The Attempt at a Solution I am not sure if I am just inputting the wrong numbers into webassign or I am just missing and important trig derivative and just completely off of the boat...

I am trying the period of 2 cosine functions that are multiplied with each other, but I am blanking out on how to find them. For example, given a function like: x(t) = cos(10*pi*t)cos(20*pi*t) I know it has something to do with the frequency of both functions (10*pi & 20*pi), but I...

Homework Statement \int cos^6(x) Homework Equations 1 = sin^2(x) + cos^2(x) The Attempt at a Solution \int cos(x) * cos^5(x) \int cos(x) * (cos^2(x))^3 \int cos(x) * (1-sin^2(x))^3 This is where I got lost, we just started this topic and I have a lot of homework to do...

How do you do stuff like sin(pi/4) in your head or sin(1) or sec(pi(x))? Thanks for your help. I'm in Calc II and fully understand the calculus but my trig foundation from high school isn't the best.

How would I go about showing \prod_{k=1}^{N-1} \sin{\frac{k\pi}{N}} = \frac{N}{2^{N-1}} I've tried using Euler's equation to substitute sin, but it just gets messy.

Homework Statement I am asked to prove the following statement is correct integral (sqrt(a^2+x^2))/x dx = sqrt(a^2+x^2)-a log(a (sqrt(a^2+x^2)+a))+ C Homework Equations x = atanθ dx = (asecθ)^2 tan^2+1 = sec^2 The Attempt at a Solution got down to a (sec^2 θ a(√sec^2)dθ)/atanθ...

Homework Statement \int x/sqrt{(x^{2}+4)} Homework Equations x=2tanx The Attempt at a Solution x=2tanx \int2tan\vartheta/\sqrt{tan^2\vartheta}+4 2/2 *\inttan/sec \intsin=-cos now is the part where i am stuck i know from using substitution that the answr should be...

1. If cylinder E weighs 30lb and theta = 15 degrees, determine the weight of cylinder F 2. Sigma F = 0 (Statics question) 3. I have gotten my separate components but I don't know how to solve the equations this sounds really stupid since I'm in calc III and physics II but my brain is just...

Show that \displaystyle{\sum_{k=1}^{n-1}\sin\frac{km\pi}{n}\cot\frac{k\pi}{2n} = n-m}\quad\quad(m,n\in\mathbb{N}^+,\ m\le n)

first off, i can solve this problem easily with u-sub but the question asks to use trig sub. \int4x/(x2+1) then i have x=tan(theta) dx=sec2(theta) =\int4tan(theta)sec2(theta)/(tan2(theta)+1) =\int4tan(theta)d(theta) =-4ln(cos(theta))=-4ln(cos(arctan(x))) thanks for the help...

Homework Statement Sec(x)/((ln(tan(x)+sec(x))^1/2) We were instructed to find the integral Homework Equations Here is a link to the wolfram solution, i don't understand the steps they...

Hi, I am a biology major starting my freshman fall quarter in about two weeks. I have always struggled with math (mostly due to a lack of effort). However, over the summer, I have made huge strides in my progress as I have been working extremely hard to master algebra and pre-calculus in...

I am currently taking Calc II and we are doing trig substitutions at the moment. I seem to have forgotten almost all the important trig identities. I understand that this sounds like something I should google but I honestly cannot find a good list of the trig identities I should know at this...

Is there a way to calculate the period of a trigonometric series (like the one below) analytically? x(t)=5sin(16t)-4cos(8t+3.1)

I know the sin(arccos(x)) = (1-x^2)^0.5 I was wondering what some of the others are: cos(arcsin(X)) tan(arcsin(X)) tan(arccos(x)) sin(arctan(x)) cos(arctan(x)) also the reverse: arcsin(cos(x)) arcsin(tan(X)) arccos(Sin(X)) arccos(tan(X)) arctan(sin(X)) arctan(cos(X))