Trigonometric Definition and 1000 Threads

Homework Statement The problem is: integrate: (1/(4x2+4x+5)2)dx Homework Equations The Attempt at a Solution 4x2+4x+5=(2x+1)2+4 gives: ∫dx/((2x+1)2+4)2 use regular substitution: u=2x+1 du=2dx dx=1/2du gives: 1/2∫du/(u2+4)2) trigonometric substitution: u=tan(z)...

My lecturer keeps simplifying trigonometric integrals in one line such as \int^{2\pi}_{0}sin^{4}(t)dt=\frac{3\pi}{4} and writes pascals triangle next to it. Just wondering what's the link between them? I'm sure it's obvious and easy, I'd just like to have an fast way of dealing with these

Homework Statement Determine all points on the function y=\sin2x-2sinx where the tangent is parallel to the x-axis.Homework Equations f'(sin(x)) = cos(x) chain rule: f'(f(g(x)) = g'f + f'g The Attempt at a Solution y=sin2x-2sinx y\prime=cos(2x)(2)-[2cosx+0sinx] y\prime=cos(2x)(2)-2cosx If...

Homework Statement [B]Evaluate \underset{x\to 0}{\mathop{\lim }}\,\frac{\sec \frac{x}{2}-1}{x\sin x} , WITHOUT using l'Hôpital's rule. Homework Equations The Attempt at a Solution Hello there, I tried to evaluate this limit using two different approaches, both of which still...

Homework Statement Find the integral of cos4 xdxHomework Equations cos2x = 2cos2x-1 cos2x = (cos2x+1)/2The Attempt at a Solution I tried using cos4x = cos2x * cos2x and i simplified it to cos4x = ((cos2x)2 + 2cos2x + 1)/4 I'm not sure if this is right. How do i go about getting the integral...

Homework Statement \int 41(sin^{6}(x))(cos^{3}(x)) Homework Equations The Attempt at a Solution I think you are supposed to use the half angle identities and then maybe integration by parts but I am lost on it.

Homework Statement Homework Equations The Attempt at a Solution After substituting: Using I'm stuck here: I can't seem to find anything online about this substitution. Any help would be appreciated. thanks.

Homework Statement Solve for t sin3tcost+cos3tsint=-1/2 Homework Equations Sum and Difference Identities The Attempt at a Solution I saw this problem the the sum identity sin(\alpha+\beta) looked like the way to begin solving for t. This condenses to sin(3t+t)= -1/2 which...

So, my question is really simple. What are the requirements for a1, a2, C1, C2 for a real solution to exist for the following system of equations? sin(theta1) + a1*sin(theta2) = C1 cos(theta1) + a2*cos(theta2) = C2 If it would be helpful, I'm not interested in the solution, necessarily (could...

I'm looking over the differential equation describing a hanging cable in a textbook, and I probably need to review my trigonometric derivatives and integrals again because I'm not seeing how they got the following: \frac{dy}{dx} = tan(\phi) \frac{ws}{T_0} \frac{d^2y}{dx^2} =...

I have three problems that I'm having a hard time with. I'd appreciate any help with any of the three problems. \int((cos(x))^6)dx AND \int(x^3 * sqrt(x^2 - 1) AND Solve for y (separation of variables): dy/dx = ((2y +...

Homework Statement I have three problems that I'm having a hard time with. I'd appreciate any help with any of the three problems. \int((cos(x))^6)dx AND \int(x^3 * sqrt(x^2 - 1) AND Solve for y (separation of...

This is from Thomas' Calculus Early Trancendentals, Media Upgrade, page 108, #27: The limit as x approaches 0 of (x csc(2x))/cos(5x) The answer is 1/2, which graphing confirms, but hell if I know how to get rid of the 5x and still come up with 1/2. It is boggling my mind. Any help would be...

Homework Statement I need to calculate the integral: \int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\mathrm{d}x Homework Equations The Attempt at a Solution There is a tip: "try substituting y=\frac{\pi}{2}-x. I tried it and didn't get anywhere. I also tried several...

sin x. d(sin x)/dx = cos x. d(cos x)/dx = -sin x. d(-sin x)/dx = - cos x. d(-cos x)/dx = sin x. i. i^2 = -1. i^3 = -i i^4 = 1 i^5 = i. I know there is a relationship between trig, the complex numbers, and exponential functions. Is there a relationship between the pattern shown here?

Homework Statement I'm not sure if you can ask about two questions in one thread; they are very similar. If it's not allowed I can make a second thread and edit this one. Simplify the expressions: 1. sin^3 theta + cos^3 theta / sin theta + cos theta 2. 2-tan theta / 2 csc theta-sec...

Homework Statement Evaluate: \int\frac{1}{(4 - \tan^2{x})^{3/2}}dx Homework Equations I must integrate the above equation using only trigonometric subtitutions of algebraic equations. The Attempt at a Solution Here is what I have so far: Let \tan{(x)} = 2\sin{(\theta)} x =...

1. (A) sin(-x) = - sin x (C) cos(x+y) = cosxcosy - sinxsiny (B) cos(-x) = - cos x (D) sin(x+y) = sinxcosy + cosxsiny Use these equalities to derive the following trigonometric identities. a. absolute value of cos x/2 = \sqrt{}1 + cosx/2 b. absolute...

how to solve eqn1 = sin((alpha)*a)*cosh((alpha)*b)=sin(alpha)*a eqn2 = sinh((alpha)*b)*cos((alpha)*a) = b*sin(alpha) alpha = 0 to 2pi... Find a & b... Plz help me with any method that would help solving this...

:blushing: using excel (vista) how can I reverse the number to be in degrees rather than radians if I want to use trigonometric functions? I have to reverse the number of the angle in radian to use those functions and I want them to be in degrees, anyone know how, thanks in advance.

Homework Statement \int cos^{2}(2x) dx Homework Equations The Attempt at a Solution After doing all of the steps I came out with \frac{x+sin4x}{8}+c In the text it says the answer is \frac{x}{2}+\frac{sin4x}{8}+c Where did I go wrong?

Homework Statement Find the limit as x approaches 0 of f(x) = 3x / sin 5x Homework Equations I might have to use the fact that "the lim of x approaches 0 of sin x/x = 1" The Attempt at a Solution I don't know how to start to solve the expresion, I would appreciate any...

Homework Statement Use an appropriate substitution and then a trigonometric substitution to evaluate the integral: \int_-^{ln(4)} \frac{e^{t}dt}{\sqrt{e^{2t}+9}} Homework Equations Seems to be close to the t=atan(\theta) model \int \frac{e^{t}}{\sqrt{a^{2}+x^{2}}}dt The Attempt at a...

Prove 1+1=2 using trigonometric functions

Part 2, leading on from https://www.physicsforums.com/showthread.php?t=315803" Homework Statement Given f(x)=cotx+tanx find \int{[f(x)]^2}dx The Attempt at a Solution I've attempted many different varieties of approaches to the problem. Trying to use the substitution method for sinx...

Homework Statement If f(x)=cotx+tanx then find \int{f(x)}dx The Attempt at a Solution I was able to manipulate (not sure if in the right direction though) the function and resulted with f(x)=\frac{2}{sin(2x)} I've also tried re-arranging things in a different way, but came up with...

Is there any trigonometric function f(theta) where theta is an angle such that f(Pi-theta)=-f(theta) and such that its square (i.e f(theta)^2) is maximum at Pi/2? Thanks

Homework Statement What is the maximal value of f(x) = sin(x) - \sqrt{3} cos(x) such that 0 <= x < 360? The Attempt at a Solution To raise to power to two f^2 = sin^2(x) - 2 \sqrt{3} sinx cosx + 3cos^2(x) I obverse that the last term has the greatest coeffient so I maximise...

Homework Statement Hi guys ,, i have the following question (it's in the attachment) : Find m and M such that m <= x sin x <= M if 0 <=x <= pi. (Any reasonably good bounds will do, I am not asking for the best possible bounds.) Hence find bounds on the value of the integral[x sin(x),0 to...

Homework Statement Pardon me first of all for any mistakes, I study in a French school so I might use incorrect terms I have to find the solutions for the following formula: sin^2 ( x - pi/4 ) = 1 Homework Equations None? The Attempt at a Solution I've mostly only worked with...

Homework Statement cosx - cosy=-2 sin(x + y/2) sin(x - y/2) Homework Equations dont know what identities to use The Attempt at a Solution ok so when i figure it out, the RHS always comes out to either... (cos x sin y - sin x cos y)/2 or just cos x sin y - sin x cos y...

Homework Statement 1) sin(x+y)sin(x-y)=cos^2y-cos^2x 2) tan(∏⁄4+x)+tan(∏/4-x)=2sec2x 3) cosx-cosy=-2sin(x+y/2)sin(x+y/2) 4) 2cotx-2tanx=4-2sec^2x/tanxHomework Equations all trig identitiesThe Attempt at a Solution 1) i understand that i should show what i have attempted but there is way too...

Can anyone please give me some idea for this problem? The instantaneous power, p, in an electric circuit is given by p = iv, where v is the voltage and i is the current. Calculate the maximum value of power in the circuit if v=0.02 sin(100 pi t)volts and i=0.6 sin(100pi t+ pi/4 ) amp...

Homework Statement Solve sin^2(x) = cos^2(x) over the interval [0,2pi] The Attempt at a Solution sin^2(x) = cos^2(x) sin^2(x) = 1-sin^2(x) 2sin^2(x) = 1 sin^2(x) = 1/2 = pi/6 sin(x) = sq root 1/2 = sq root pi/6 Unfortunately I am completely lost at this point and am not sure if I...

Homework Statement cosx/(secx+tanx) The Attempt at a Solution So far I have this: =cosx/(1/cosx + sinx/cosx) =cosx/(sinx + 1/cosx) =cos2x/sinx + 1 From there I don't know what to do. I've messed around with it for a while but don't seem to get anywhere. Any help is appreciated.

Hi everyone Could you give me a way to calculate the period of every trigonometric functions? thanks

Hi all, I was tutoring someone in Algebra III today and encountered a problem that threw me for a loop. (cos x)^4 = cos (x^2) Is there a way to solve this algebraically?

Homework Statement Simplify the following. Write all trigonometric functions in terms of t. Homework EquationsThe Attempt at a Solution I know that: sec(t+2pi)=sec(t) 1+tan(t+3\pi)= 1+tan(t) What about: csc(t-6\pi)? Will it be equal to csc(t). Can anyone please help me with this? Thank you...

Homework Statement solve the inequality: -1\leq 1/(1+cosx) \leq1 The Attempt at a Solution firstly cosx does not equal -1 but you'll see doesn't help much -1<cosx<1 0<cosx+1<2 that makes the above equation 1/(1+cosx) between 0.5 and infinity. but I have no...

Homework Statement Let f(x)=cos (x). Denote f^2(x) = ff(x), f^3(x)=fff(x) and so on. For x=100 radians, find f^n(x) for n=1 to 20 Develop a calculator technique to find f^n(x) for any given value of n. Hence, find correct to 7 decimal places, the limit of f^n(x) for x= 100 radians and n...

Hi All, I’m currently attempting to work ahead on my precalculs and I’m looking at trigonometric equations. I seem to have a bit of a problem with this example (i haven’t had too many issues with the rest of the exercises), 9cos(2x)+sin(x)=9 (solve for x in the interval 0 <=x <=2pi.) I’m...

Homework Statement A road is built up the slope of a hill with a height of h meters and an angle of inclination of x. The length of the road is d. a) Sketch a diagram of this situation. Label all quantities. b) Show that the length of the road is represented by the relation d = h csc x. c)...

Is there any standard way to do this? Specifically, I know the equation I'm looking for is a cosine function, and I know two points. Is there a way to find the equation of the cos function which has been translated and compressed given only these two points?

Homework Statement Two curves y_1=(\frac{20}{x^2})\sin(\frac{10}{x}) and y_2=5\cos x intersect in three points in the interval (1,3). Draw the graphs, compute the minimum and maximum points as well as the turning points and show the points of intersection. 2. The attempt at a...

I’ve got this tricky trig substitution that I’ve been trying to do as for my Calc II class. I think that I’ve done the substitution part right I just have no idea where to go from here. I’ve tried many routes including integrating by parts as well. Please help me thank you...

Homework Statement \frac{secx-cscx}{secx+cscx}=\frac{tanx-1}{tanx+1} \frac{(tan^{2}x - cot^{2}x)}{(tanx + cotx)}= (tanx - cotx) tan^{2}2x+sin^{2}2x+cos^{2}2x=sec^{2}2x cot^{2}2x+cos^{2}2x+sin^{2}2x=csc^{2}2x The Attempt at a Solution I've tried many times in my notebook and I'm...

Homework Statement http://img135.imageshack.us/img135/4150/trighelp.jpg Homework Equations The Attempt at a Solution http://img18.imageshack.us/img18/8480/workz.jpg Please help I'm totally confused, if anyone can help I can offer a reward of monetary value :).

Homework Statement http://img135.imageshack.us/img135/4150/trighelp.jpg Homework Equations The Attempt at a Solution http://img18.imageshack.us/img18/8480/workz.jpg Please help I'm totally confused, if anyone can help I can offer a reward of monetary value :).

Homework Statement Use the function f(x) = sin x + cos x, where 0<=x<=pi to answer the following. a) Determine all stationary points. Classify the points as minimum or maximum b) locate the points of inflection c) determine the endpoints of the interval Homework Equations...

Im having trouble with this problem here: x-->0 tan6x / sin2x So far I only have: (sin6x / cos6x) / (2sinx cosx) What would be the next step? Multiply the reciprocal? Also, could somebody tell me if I am doing this problem right? x--> 0 (sin (cosx)) / secx sin (cosx) / 1/cosx...