Trigonometric Definition and 1000 Threads

Homework Statement The integral from 0 to pi/2 of 1/(1 + (tanx)^sqrt2) dx. Homework Equations trig identities? The Attempt at a Solution I tried some substitutions but it just made the problem more complicated. I also multiplied by (tanx)^sqrt2 in the numerator and denominator in...

Homework Statement sin 2θ = sin θ Find the solutions in degrees. Homework Equations sin 2θ = 2sinθcosθ The Attempt at a Solution sin 2θ = sin θ 2sinθcosθ = sin θ sinθ *cosθ/sin θ = 1 That's as far as I can get, and I think that is wrong. How do I procede from 2sinθcosθ = sin θ?

Can anyone help solve the below for 'a' 0=b(ycos(a)-bcos(2a)+xsin(a)) I've reduced it to b=ycos(a)+2sin(a)sin(a)+xsin(a) =sin(a)(cot(a)+2sin(a)+x) Which I think is right, but I can't get any further without just ending up with different forms that appear more complex.

Homework Statement Hi all. Today I had to solve: \cos \theta = -1/2. What I did was to look in a table to find that \theta = 2\pi/3 \quad \text{and}\quad \theta = 4\pi/3. My question is what is the general strategy when I wish to write this as a a function of an integer n? Is there even a...

Hey there This is a trig substitution for my Calculus 2 class and I really have NO idea how to get started... \int\frac{4}{\sqrt{3-2x^2}}dx My professor has yet to go over how to evaluate trigonometric substitutions with coefficients in front of variables.

Hi guys, I need to solve the following trigonometric equation. Some time ago I would have used Fortran with the appropriate libraries but now I was wondering whether there is any better approach. Any suggestion? w^2/c^2= k//^2 - Sqrt(w^2 Eps_b^2/c^2 - k//^2) * Tan[Sqrt(w^2 Eps_b^2/c^2 -...

Hi Everyone, Do there exist any explicit formula for Cos(x_1+x_2+...+x_n) as a sum of products of Sin(x_i) & Cos(x_i)? Or we need to expand using Cos(A+B), Sin(A+B) again & again? If it exists then what is about Sin(x_1+x_2+...+x_n)? [It is understood that there will be 2^(n-1) number of...

Homework Statement sqrt3 cot 3x + 1 = 0 where 0 _<x_<2pie Homework Equations The Attempt at a Solution I narrowed it down to a constant on one side, cot 3x = -1/sqrt3 which I could turn into cos x/sin x = -1/sqrt3 but I have no idea where to go from here. Any help...

Homework Statement tan x + 1/tan x - 1 = sec x + csc x/sec x - csc x Homework Equations The Attempt at a Solution Ive tried working with the right side and have gotten as far as sin x/cosxsinx - cos x/cosxsinx Im not sure if I am just out to lunch, or on the right track...

Homework Statement (tan2x) - (sin2x) = (tan2x)(sin2x) Prove these two are equal. Homework Equations Various trig identities, mainly tan2x = sin2x / cos2x The Attempt at a Solution I tried putting in Sin2x / cos2x for tan, but I don't know where to go from there. Anyone mind...

\frac{dx}{dt} = \cos(x+t) I'm having real troubles with this; I tried a substitution of u=x+t but it just ends up as, t=\tan{u} + \csc{u} + C And I can't see where to go from there. (the middle function is cosec; it didn't come out very clearly on my screen).

Homework Statement Prove that sin (a+b) does not equal sin a + sin b. Let a = pi/3 and b = pi/6 Homework Equations The Attempt at a Solution Where I am lost is how to figure out what pi/3 or pi/6 is. Like for example, how can I know sin pi/3 is sqrt3 over 2? Is this a...

Homework Statement Let y = tan2(3x-2) Find dy/dx The solution is: 2*tan(3x-2)*sec(3x-2)*3 = 6*tan(3x-2)*sec2(3x-2) Why is it not: 6*tan(3x-2)*sec(3x-2) I am thinking: y = (tan(3x-2))2 take the power 2 down,multiply with the parentes multiply with the defferentiated parentes...

I encountered a few problems for a few questions while doing my homework. 1. Angular measure problem: A Ferris wheel with a radius of 25.3m makes 2 rotations every minute. a) Find the average angular speed of the Ferris wheel in radians per second. b) How far does a rider travel if the ride...

Homework Statement \int1/sqrt(1-(x+1)^2) dx 2. The attempt at a solution I think a=1 but don't know what to set u equal to.

I need to find the limit of sin(3t)^2/t^2 as t approaches 0. We have not yet learned L'Hopital's rule, so how do I find the limit here? I tried to take the derivative of sin(3t)^2/t^2, but it is nowhere near cancelling out 't' from the bottom. Thanks

Homework Statement Be x an element in the interval [Pi/4, 3Pi/4] express cos(2x), sin x, sin (x+pi) in terms of x. You must know that, for this question, cos x = z and z will always be < 0. Homework Equations cos(2x) = 2 (cos(x))^2 - 1 cos(2x) = cos^2 x - sin ^2 x sin^2 x + cos ^2 x = 1...

Why is cos^2 x = \frac{1}{2} + \frac{cos(2x)}{2} ?

Homework Statement Using trigonometric substitution, verify that \int \sqrt{a^2[-t^2}dt (INTEGRAL FROM 0 TO \pi)=(1/2)a^2sin^{-1}(x/a)+(1/2)x\sqrt{a^2-x^2 Sorry it doesn't seem to want to allow me to place superscript inside a square root. but inside the first sq. root is a2-t2 and the...

Homework Statement prove : 1-cos x / sin x = sin x / 1+cosx 1-cosx / 1+cos x = tan^2 (x/2) Homework Equations The Attempt at a Solution I have No idea how to solve it

Homework Statement \intsin3cos2xdx The Attempt at a Solution I've successfully solved this problem by factoring out 1 sinx and changing the sin2x to (1-cos2x then assigning u=cosx and du=-sinx and so on. What I'm wondering is why does letting u=sin3x in the original integral not...

Hi everyone, I would like to know, since the lim theta --> 0 (sine theta / theta) = 1, what is the limit theta --> 0 of cosine and tangent? Thank you very much in advance

Homework Statement I'm trying to do a few problems that ask me to "find the point (x,y) on the unit circle that corresponds to the real number t." Examples of these problems are: t = pi / 4 t = 7pi / 6 t = 4pi / 3 etc etc Homework Equations The Attempt at a Solution I...

I'm trying to solve: sin2x = -cos2x so my first step was... 2sinxcosx = -cos^2x - sin^2x and then... 2sinxcosx + cos^2x + sin2x = 0 but I'm confused on how I would end up factoring 2sinxcosx + cos^2x + sin2x, or if I did something wrong earlier in the problem...thank you

Homework Statement tanX+tan Y / 1-tanXtanY= cotX+cotY/cotXcotY-1 Homework Equations tan= sin/cos cot= cos/sin The Attempt at a Solution

Homework Statement verify the identity : 1+sec(-∅)/sin(-∅+tan(-∅) = -csc ∅ Homework Equations The Attempt at a Solution 1+sec∅/-sin-tan∅ = -csc∅ I don't know where to start from, does anyone have any idea?

A confusing trigonometric question! Hi guys, I had a question. I was given the following equality. There was no problem statement that came with it (i.e. it did not say solve the equation or prove the identity, or anything of this nature) sec x + csc x / tan x + cot x = sin x + cos x The...

Homework Statement My problem from before has been more or less resolved, but now I have a new, bigger problem. I need to figure out how to find recuring values for trig functions. I'm having a hard time figuring out how to 1. Get the equations associated with a given value for the trig...

cosx/1-sinx + 1-sinx/cosx = 2secx + 2tanx I can get to 2secx + tanx - tanx, any help is appreciated

Pendulum Ride - Trigonometric Function Homework Statement At Canada's Wonderland, a thrill seeker can ride the Xtreme Skyflyer. This is essentially a large pendulum of which the rider is the bob. The height of the rider is given for various times: Time(s) 0 1 2 3 4 5 6...

Homework Statement I have this integral to solve: \int \frac{ab}{a^2 cos^2 t + b^2 sin^2 t} dt The limits are 0 to 2*pi. Homework Equations The Attempt at a Solution I've tried using trigonometric identities, trigonometric substitution... and many kinds of algebraic...

Hello, I have been wokring on this problem for some hours now, and I get the wrong answer, but I can't understand why, could you guys please look at it? http://img219.imageshack.us/my.php?image=utennavnwv7.jpg

[SOLVED] A Trigonometric Identity Probelm If I have sin^2 2x would I be able to apply the identity sin^2x = (1/2)(1-cos2x) to get this: sin^2 2x = 2(1/2)(1 - cos^2 x) Similarly, if I had sin^2 2x + cos^2 2x would I be able to use the identity sin^2 x + cos^2 x = 1 to get: sin^2 2x +...

Homework Statement ∫dθ/(1 + (sinθ)^2 ), [0, π] Homework Equations Cauchy's Formula, perhaps Cauchy's Thm. http://mathworld.wolfram.com/CauchyIntegralFormula.html http://mathworld.wolfram.com/CauchyIntegralTheorem.html The Attempt at a Solution I first substituted sinθ =...

Homework Statement Solve the integral using trigonometric substitution. \int\frac{\sqrt{4x^{2}+9}}{x^{4}}dx Homework Equations 2x=3tan\theta x=2/3 tan\theta dx=2/3 sec2\thetad\theta \sqrt{4x^{2}+9}=3sec\theta The Attempt at a Solution \frac{8}{9} \int...

Homework Statement Lim (1-cosX)/X^2 X->0 Homework Equations Not 100% sure try to use the following identity: sin^2(X)=(1-cosX)(1+cosX) or sin^2(X)=1-cos^2(X) The Attempt at a Solution Tried substituting (sin^2(X))/(1+cosX)) for 1-cosX but that didnt help and so for the last half...

Why are wave functions, e.g., Schrodinger's, based on the complex exponential function (e^{}ix) and not trigonometric functions (sine or cosine)? See Euler's formula for their relationship: http://en.wikipedia.org/wiki/Euler%27s_formula Furthermore, by using the complex exponential...

Homework Statement \int \frac{e^{3x}dx}{\sqrt{1-e^{2x}}} Homework Equations The Attempt at a Solution Alright so I am able to do other similar problems fine, I think it is the "e" that is throwing me off as well as the fact that the "x" is in the exponent. I started the...

Hi, I'm working with finding the derivatives of trigonometric functions but I'm not confidant with some of my answers. if someone would go over these derivatives i would appreciate it. thanks in advance! determine \frac{dy}{dx} . do not simplify. question 1 y = sec \sqrt[3]{x} my...

Hello, i'm having some trouble with evaluating limits if anyone could help me out a bit i would appreciate it. thanks in advance evaluate the following limits: Question 1: lim x -> 0 \frac{2tan^{2}x}{x^{2}} my answer: u = x^{2} as x -> 0 u-> 0 = lim u->0...

Hi, We were going over trigonometric integration in Calculus II the other day. I got the basic idea, but get lost when we're doing the u-substitution. We had a problem like this: \int cos^3 (x) dx Then we did: \int (1 - sin^2 (x)) cos(x) dx Starting u-substitution: u =...

y = sin( 4 x ) cos( 3 x ) f(x) = sin4x g(x) = cos3x f'(x) = cos4x g'(x) = -sin3x And by using the product rule, i'll get: cos4x(cos3x) - sin4x(sin3x) Is the answer correct or can be simplify again??

Homework Statement If cos x = a/b and tan x = c/d; where a, b, c do not equal 0, then sin x is... (a) bd/ac (b) bc/ad (c) ad/bc (d) ad/bc Homework Equations The Attempt at a Solution The way I see it, if cos x = a/b, then b=hypotenuse. if tan x = c/d, then d=...

Homework Statement The graphs of f( ) = 2sin() - 1 (blue) , and g() = 3cos() + 2 (red) are shown below: http://img403.imageshack.us/img403/6991/38ah7.jpg http://g.imageshack.us/g.php?h=403&i=38ah7.jpg What equation would have the intersection points of the graph its solutions...

Homework Statement ∫sec^6 t Homework Equations sec^2 (x)=1+tan^2 (x) The Attempt at a Solution ∫ (sec^2 (t))^2 * (Sec^2 (t))^2 ∫(1+tan^2 (x))^2 (1+tan^2 (x)) ∫(1+2tan^2 (x) +tan^4 (x)) (1+tan^2 (x)) u=tan (x) du=sec^2 dx i'm stuck now

Homework Statement ∫sec^2 (x) * tan (x) dx Homework Equations sec^2 (x)= 1+tan^2(x) The Attempt at a Solution =∫(1+tan^2 (x) or tan (x) tan (x)) tan (x) dx u=tan x, du=sec^2 dx ∫ (1+u^2) u du = ∫u+u^2)du = u^2/2 + u^3/3 = 1/2 tan^2(x)+ 1/3 tan^3 (x) +c the...

Homework Statement ∫ cosx+sin 2X/sinX Homework Equations sin^2 x =1/2 (1-cos2x), cos^2=1/2 (1+cos2x) if cosine is odd, u sin x, cos^2 x=1-sin^x) , if sine is odd u=cosx sin^2x =1-cos^2x) The Attempt at a Solution i'm not sure how to start this one because I've never came...

Homework Statement ∫1/x^2*√25-x^2 Homework Equations √a^2-x^2 , x=a sin (theta) , -pi/2 less than or equal theta less than or equal pi/2 Identity 1-sin^2 theta= cos^2 theta table of trigonometric substitutions The Attempt at a Solution x=5 sin theta dx= 5...

Homework Statement Solve: 5sin(x) + (2 * squrroot 3) = (squarroot 3) + 3sin(x) Homework Equations sin (60) = square root 3 / 2 C.A.S.T. rule The Attempt at a Solution 5sin(x) + (2 * squrroot 3) = (squarroot 3) + 3sin(x) 5sin(x) - 3sin(x) = (squarroot 3) - (2 * squrroot 3)...

Homework Statement http://img206.imageshack.us/img206/9099/titleol2.jpg http://g.imageshack.us/g.php?h=206&i=titleol2.jpg Show the above statement is equivalent to : sec (2x) + tan (2x) Homework Equations The Attempt at a Solution First attempt in which I used the...