Trigonometric functions Definition and 165 Threads

I've read a bit about constructibe polygons, and that a regular n-gon can be constructed with compass and straightedge if and only if trigonomatric functions of 2π/n can be expressed with square roots and basic arithmatic alone. That is possible if and only if n is the product of distinct Fermat...

Hello, What's the easiest way to evaluate an integral like this? \int_{\frac{-\pi}{2}}^{0}\cos^{10}x dx The only method I can think of is to expand the \cos^{10} x using trigonometric identities, and getting \frac{1}{32}\left(1-\cos2x\right)^5. I tried subbing u=1-\cos2x but I doesn't seem to...

Homework Statement Find the second derivative (y") of y=xtanx. The attempt at a solution I got the first derivative (y') y=xtanx y'=x(secx)+tanx I started the second derivative and got stuck y"=xsec^2x+tanx

is there any definite way of finding the period of non trigonometric functions? can we use f(x+t)=f(x) and solve for t from this equation?

Homework Statement I want to express sin(x) in terms of tan(x).Homework Equations tan(x)=sin(x)/cos(x) 1+tan2(x)=sec2(x)The Attempt at a Solution sin(x)=cos(x)tan(x) At this point I realize this is assuming x\neq \pi/2+k\pi cos^2(x)=\frac{1}{1+tan^2(x)} therefore...

Homework Statement Is there a way to determine the period of a function like f(x) = a*sin(b*x)^2 + c*cos(d*x)^2 + e*sin(f*x) + g*cos(h*x)? Homework Equations The Attempt at a Solution I know how to find the periods of sines, cosines, and arbitrary sums of the two, but the...

Homework Statement ∫dθ/(1+βcosθ)^2 ; -1<β<1 θ=0 to 2pi Homework Equations The Attempt at a Solution attempt solution: 1) make substitution: dθ=dz/iz Z=e^iθ cosθ=1/2(Z+1/z) 2) substitute: 1/i*dz/(β+Z(1+(β^2)/2)+((3βZ^2)/2)+((β^2)Z^3)/4)+((β^2))/4Z) 3) Next ...

Limits of Trigonometric Functions. URGENT! Homework Statement Evaluate stackrel{lim}{x \rightarrow0}[/tex] [sin(\frac{2e}{x3}) \bullet (arctanx)] Homework Equations All I know is that the equation stackrel{lim}{x \rightarrow0}[/tex] \frac{sin x}{x} = 1 might be helpful, but I'm not sure...

Homework Statement Find the constants A and B such that the function y = Asinx + Bcosx satisfies the differential equation y'' + y' - 2y = sinx Homework Equations None The Attempt at a Solution My attempt: y = Asin x + Bcosx y' = Acosx - Bsinx y'' = - Asin x - Bcosx y''...

Hi, can you help me solve these three questions? Please show each step. Thanks. 1. solve for x: arcsin(6x-pi)=1/8 2. Find an equation of the tangent line to the graph of y = arcsin (6x) at the point ((1/(6sqrt2),(pi/4)) 3. Find the indefinite integral of 1/sqrt(81-100x^2)

Homework Statement I'm in an Intermediate Mechanics course right now, and while the Physics itself isn't giving me too much trouble, I am lagging behind in the Math department. I am trying to solve the integral: \int cos(\omega t) sin(\omega t - \delta) dt Homework Equations...

cosh x= e^x+e^-x/2 sinh x= e^x-e^-x/2 Can someone explain why the hyperbolic trigonometric functions are defined in terms of the natural exponential function, e^x ?

Homework Statement Cos^2x-Sin^2x/2 SinxCosx The Attempt at a Solution I changed cos^2x to 1- sin^2x which then the equation was 1- s sin^2x/2snxcosx and i have no idea how to make this a single trig. function

Homework Statement how to show using MVT that cos(cos x) is a contraction. Homework Equations | d/dx (cos(cos x)) | = | sin(cos x) sin(x) | < sin 1 < 1 The Attempt at a Solution Using that relation, the original problem is easily solved. My question is, how do we know: |...

Homework Statement How can I integrate this: \int sin (nt) sin (n \pi t) dt This actually in the Fourier series.

Homework Statement True or false? lim Tanx/(1-Cosx) = lim Sec2x/Sinx = Infinity (limits are as x approaches \pi from the left) The Attempt at a Solution I tried just plugging \pi into x in the first limit, and I ended up getting 0/2, which exists but is just 0. So...

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

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...

Prove 1+1=2 using trigonometric functions

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

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)...

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...

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...

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...

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 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...

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 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...

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...

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...

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...

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 I'm learning now about darivative all by my self (without a teacher) and I'm not sure about this development Homework Equations The Attempt at a Solution Y=senx y+{\Delta}Y=sen(x+{\Delta}Y) {\Delta}Y=senx*cos{\Delta}x+ sen{\Delta}x*cosx What about...

Homework Statement lim x --->0 [tan(2+x)^3 - tan8]/x Homework Equations f'(a)=lim h-->0 f(a+h)-f(a)/h The Attempt at a Solution should i differentiate first? am i allowed to do that?

[SOLVED] Derivatives of Trigonometric Functions I need to find the critical numbers of this function: y = cos x - sin x where -pi <= x <= pi I found the derivative as: dy/dx = -(sin x + cos x) But when I equate dy/dx to zero, I get: sin x + cos x = 0...where do I go from here?

Hi there, I am struggling to solve for x in the following problem:- Find all values of x in the interval 0<= x <= 360 for which: tan^2(x) = 5sec(x) - 2 I have used the identity tan^2(x) + 1 = sec^2(x) to get: sec^2(x) - 1 = 5sec(x) - 2 and rearranged to get sec^2(x) - 5sec(x) +...

Why do some problems return the wrong answer while others do not on the ti-89. For example: \[ \lim_{x \to 0} \frac{\cos\theta \tan\theta}{\theta}\] Shows up wrong (shows up as pi over 180). But \[ \lim_{x \to 0} \frac{\sin x(1 - \cos x)}{2x^2}\] does not?

Homework Statement (1-cos^2x)(1+tan^2x) = tan^2xHomework Equations N/AThe Attempt at a Solution (1-cos^2x)(1+tan^2x) = tan^2x L.S. = (sin^2x)(1+sin^2x/cos^2x) = sin^2x+(sin^4x/cos^2x) Now, I get a common denominator, but it's not doing anything for me. Did I do the right thing in converting...

1.A kite 40 m above the ground moves horizontally at the rate of 3 m/s. At what rate is the angle between the string and the horizontal decreasing when 80 m of string has been let out. Answer is 0.02 m/s 2. What I did was: -Drew a triangle as prescribed above -I found the unknown...

Homework Statement Determine whether the series converges and diverges. \sum_{n=3}^{\infty}\ln \left(\frac{\cosh \frac{\pi}{n}}{\cos \frac{\pi}{n}}\right) The Attempt at a Solution \sum_{n=3}^{\infty}\ln...

Homework Statement Find d^2y/dx^2. y = x cos x The Attempt at a Solution I've been doing derivatives recently and now got into doing them with trig functions. I thought it was, y = x cos x = -xsinx = -xcosx but that is the derivative of the derivative. The problem...

Derivative trigonometric functions Homework Statement Find d^{2}x/dt^{2} as a function of x if dx/dt=xsinx Homework Equations The Attempt at a Solution I tried to solve the problem by taking a second derivative of dx/dt=xsinx but I was not sure how to start. Also, it is...

Homework Statement Three functions are defined as follows: f:x> cos x for the domain 0< (or equal to) x < (or equal to) 180 g:x> sin x for the domain 0< (or equal to) x < (or equal to) 90 h:x>tan x for the domain p< (or equal to) x < (or equal to) q Find the range of f. -1<(or...

I was doing my exam today and ran into a couple problems. First one: how do you differentiate \tan^2? I converted it into \sec^2 - 1 and used the u/v = (u`v - v`u)/v^2 method, but I would like somebody clever to do it for me, just to be sure, please. Homework Statement Another problem. Rate of...

Homework Statement I can't seem to find online how to calculate the error propogated by trigonometric functions. That is, I know the uncertainty in \theta but am not sure how to deal with it when I apply the tan function. I am quite okay with how to deal with all the basic...

I just came across a problem that wants you to solve for csc of an angle in radians... However, I'm confused about the answer given. Here is the problem: Find the csc when t=-2pi/3, which is equivalent to -120 degrees right? I got -2sqrt.(3)/3 but the answer in the back is -2sqrt.(3)/2...

I was wondering if someone would be able to help me with the following questions: -A progessive wave has amplitude 0.40m and wave length 2.0m. At a given times the displacement y=0 at x=0. Calulate the displacement at (a)t=5sec (b) t=0.8sec -A progessive wave has amplitude 2.5m and a time...