Trig functions Definition and 218 Threads

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...

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))

Homework Statement The first problem I'm having difficulty with is \stackrel{lim}{x\rightarrow0} \frac{sin x}{5x} And the second is: \stackrel{lim}{x\rightarrow0} \frac{sin x(1-cos x)}{2x^{2}} Homework Equations I assume that for the first problem I need to simplify it to the rule...

Homework Statement evaluate lim(x->0) (tan^8(t))dt(between 0 and sin^2x) Homework Equations The Attempt at a Solution [tan^8(sin^2(x))]/sin^18(x) my book says to use l'hospital's rule, so i continued with [8tan^7(sin^2x)*sec^2(sin^2(X))*2sinxcosx] but my book says i should...

Homework Statement Which one is not periodic? (a)|sin 3x|+sin2x (b)cos\sqrt{x}+cos2x (c)cos 4x + tan2x (d)cos 2x+sin x Homework Equations The Attempt at a Solution I don't understand how to show whether the functions are periodic or not? :confused:

Homework Statement let g be a function mapping x to xcosx-sinx. use the mean value theorem to prove that g(x) < 0 for x in (0,pi]Homework Equations well the function is both continuous and differentiable on the interval so that's a start... The Attempt at a Solution basically i thought i'd...

Homework Statement A cargo ship is tied up at the dock. At low tide, a 12-m long unloading ramp slopes down from the ship to the dock and makes an angle of 30 degrees to the horizontal. At high tide, the ship is closer to the dock, and the unloading ramp makes an angle of 45 degrees t othe...

Homework Statement I've come across integrals of exponential and trig functions and I have no idea how to do them. Integration by parts doesn't really work because they just derive into either e or another trig function. One of them is \intsin(a)*sin(b - a)da Another is \inte(a)*sin(a)da...

Homework Statement This isn't really a question on its own, rather a step in the solution to another question: How would I prove that y= A\cos x + B\sin x (A, B arbitrary constants) has at least n zeroes in the interval [\pi , \pi (n+1)] where n\in\mathbb{Z}\;? (I don't need to be too...

Homework Statement Prove the Identity (show how the derivatives are the same): arcsin ((x - 1)/(x + 1)) = 2arctan (sqr(x) - pi/2) Homework Equations d/dx (arcsin x) = 1/ sqr(1 - x2) d/dx (arctan x) = 1/ (1 + x2) All my attempts have been messy and it may be because I didn't...

Homework Statement Does this look correct? How do I know when to stop simplifying things? Sometimes it comes out to a nice little expression, and other times it's a long solution. In the latter, I spend too much time trying to simplify it further! Homework Equations The Attempt at a...

Here's an interesting problem: How can you find the area of any normal polygon with x sides (or corners) that is inscribed in a circle of radius 1? No trig functions, or things like e or π (Pi), or infinite series, are allowed. If possible, try to avoid summation notation as well, but that might...

is it meaningful to evaluate cos and sin at infinity? I ask in relation to Fourier integrals... ie does cos(infinity) have a value

Homework Statement Y = - sin (2X) Homework Equations The Attempt at a Solution So.. I know how to graph - sin, that's going to be one 1 but reversed. Now my problem is the (2x). How do I graph 2x in the trig graph? How would I go about making a horizontal compression? Thank you

I'm on mobile so I can't use regular symbols. Sin80°csc80° = 1 why does this equal one? Is there multiplication involved here? I know csc = 1/sin

Homework Statement integral of x^2/sqrt(9-25x^2) Homework Equations The Attempt at a Solution dont know how to type theta so I am using @ so i made x=3sin@ dx=3cos@d@...

Homework Statement Determine the average rate of change of the function y = 2cos (x - pi/3) + 1 for the following internal: pi/2 < x < 5pi/4 Homework Equations AROC = [ f(x2) - f(x1) ] / x2) - x1 The Attempt at a Solution For an approx. value, I would set the calculator in...

Homework Statement Is 3cos22x + cosx2 - 1 a polynomial function? Homework Equations The Attempt at a Solution

Trig Functions - "When wil object be 9cm below 0?" Homework Statement Here is the background information: A weight hanging from a spring is set in motion by an upward push. It takes 10 s for the weight to complete one cycle from moving 12 cm above 0, then dropping 12 cm below 0...

Homework Statement An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle θ with the plane, then the magnitude of the force is given by the following equation, where μ is a constant called the coefficient...

Homework Statement Determine sin(arctan(3)) The Attempt at a Solution I do not know how to start this. No special triangles : (.

Homework Statement The Attempt at a Solution No attempt, don't even know where to start. I get a point... I can draw a triangle out of it. I can figure out the X and the Y. I know the 6 equations... Sin, Cos, Tan, and the opposites Cosecant, Secant, and Cotangent... I know...

Homework Statement Find the general solution of: a) sin x = 1/\sqrt{2} b) cos x = 0.5 The Attempt at a Solution a) x = asin(1/\sqrt{2}) x = (π/4) + 2nπ b) x = acos(0.5) x = π/3 + 2nπ Basically, my strategy was to solve for the basic angle, and then add multiples of the...

Homework Statement I'm given the problem: \int\frac{\sqrt{y^{2}-25}}{y} dy Homework Equations I set y = 5sec(u), and solve for the subsitution. The Attempt at a Solution At the culmination of my solution, I achieve: 5tan(u) - 5u + C Here is my dilemma, u stands for...

Homework Statement I need help evaluating the integral Cotx3/10 I factored out the 1/10 from the integral and am just left with (1/10)*Cotx3 from here i do not really know what to do. I rewrote it in terms of sine and cosine to get (1/10)*(Cosx3/Sinx3)dx I multiply the integral...

Homework Statement sin(tan-1(x)) Homework Equations The Attempt at a Solution y=tan-1(x) tan(y)=x sec2(y)= 1+tan2(y) sec(y)=\sqrt{1+x^2} This is where I'm getting stuck. I know that I have to say that the sin(y)= whatever, but I'm not sure how to tie the sin sec and tan...

Homework Statement Find \int(x+2)dx/sqrt(3+2x-x2) Homework Equations \intdu/sqrt(a2 - u2) = sin-1u/aThe Attempt at a Solution I began by completing the square: 3+2x-x2 = 4 -(x2-2x+1) So, 4-(x-1)2 = a2-u2 and a=2 and u=(x-1) Further, since x=(u+1), dx=du and (x+2)=(u+3) Substituting, I...

Homework Statement Differentiate e^x * cotx / 5sqrtx^2 [Sorry for not using the formatting things. They didn't seem to be working for me, and this is urgent!] Homework Equations The quotient rule seems like that's the way to go... The Attempt at a Solution At first I tried using...

Hi. I'm having trouble trying to understand the relationship between inverse trig functions, especially arcsin x, and pythagorean identity. I know that because cosx=sqrt(1-(sinx)^2), derivative of arcsin x is 1/(cos(arcsin x)) = 1/(sqrt(1-(sinx)^2)arcsinx)) = 1/(sqrt(1-x^2). But how does...

x in (0,pi]; f(x) = sin(x)-x2; f'(x) = cos(x) - 2x; f'(x) = 0 ==> cos(x) - 2x = 0; since |cos(x)| ≤ 1, cos(x) - 2x ≤ 1 - 2x; Now 1-2x = 0 <==> x = 1/2; f'(1/4) = cos(1/4) - 2*(1/4) > 0 and f'(3/4) = cos(3/4) - 2*(3/4) < 0; ==> x = 1/2 is maximum and f'(x) ≤ 1/2; Is my...

Homework Statement solve the equation for x in the interval 0<=x<=2pi 4cos(2x)+sin(x)=4 The Attempt at a Solution I don't understand what the question is asking me to do? Where do I start and how can this equation be made into an appropriate equation so i can answer the question?

Hi there I was wondering if there is a simple way to solve for the roots of a complicated summation of trig functions that can't be combined with any simple identities. I have an equation of the form: 0 = sin(8x-arctan(4/3))+3.2sin(16x+pi/2) where the two sines have different amplitudes...

Homework Statement See attached image Homework Equations Power reducing Identy: cos^u = (1+Cos2u / 2) The Attempt at a Solution This is a problem that was done as an example (I know it is not complete it is missing the last integration step) but this is where I am getting stuck my...

Homework Statement *The sum from n = 1 to infinity* (cos(n*pi))^2/n*pi where n is the variable. Homework Equations All forms of convergence tests (i.e. Ratio Test, Integral Test, Alternating Series test etc.) The Attempt at a Solution I am having trouble figuring out which route...

Evaluate the following expressions. Your answer must be in radians. a) arctan(-(sqrt3)/3) b) arctan((sqrt3)/3) c) arctan(-sqrt3) What I got are: a) 5pi/6 b) pi/6 c) 2pi/3 Do I got these answers right?

Homework Statement there's a picture of the question... from my textbook http://photos-h.ak.fbcdn.net/hphotos..._1385551_n.jpg thers a diagram image of the problem too to help understand Homework Equations well its a word problem, i used cosine rule at beginining and then...

could someone please try and solve this? and explanation would be greatly appreciated too ! this was one of the homework questions, but i didnt really understand. the teacher explained it again to the class partly, but didnt understand a part of it so we didnt continue... maybe one of you guys...

Homework Statement (In radians I assume) Using the exact values of sin, cos, tan of 1/3 pi and 1/6 pi, and the symmetry of the graphs of sin, cos and tan, find the exact values of sin(-1/6pi), cos (5/3pi) and tan(4/3pi). Homework Equations cos(x)=sin(x+pi/2) sin(x) = sin(x+2pi)...

...are fascinating. At least I think so. Sine and cosine are the additive inverses of their respective second derivatives, for example. Astonishing! Are there any other startling properties of trig functions (not inverse trigs) that would just blow my mind? Somewhere in the beautiful...

how do i integrate -- cosx/((sinx)^2 + 1) with respect to x thanks for your help

All my life I've understood Trig Functions as ratios of sides of a triangles. With this understanding I have been able to get the ratios for simple triangles like 30, 45, etc... since my teachers made me memorize the sides of it... But now I'd like to know how would you find the ratio of a...

Homework Statement lim (cos x - 1) / (sin^2 x + x^3) as x approaches 0. Homework Equations sinx/x = 1 The Attempt at a Solution I get 0/0. Is that the answer?

Homework Statement y' = csc2(\vartheta / 2 ) Find y" The Attempt at a Solution So far, i have 2 csc (\vartheta/2) *csc(\vartheta/2)cot(\vartheta/2) * 1/2 but I'm wondering, how do you take the derivative of a half angle identity? or does it just simplify down to csc2(\vartheta...

How do you find the power series for inverse trig functions? Can I find the power series for arcsin by manipulating the power series for sin? Thanks!

Homework Statement I'm in a first-year analysis course, and this question was given by my prof. as practice for her midterm test. "Sketch the graph of the function \begin{equation*} f(x) = \text{sin} 2x + \sqrt{3} \text{cos} 2x \end{equation*} Determine the amplitude, the frequency and...

Homework Statement Integral(sinx(x)dx/(cos^2(x)+cos(x)-2) Homework Equations The Attempt at a Solution What I tried to do first was factor the denominator, so i got (cos(x)-1)(cos(x)+2) from there, I set up my partial fractions equation trying to solve B(cos(x)-1) + A(cos(x)+2) =...

Homework Statement lim as x approaches 2 (cos(pi/x))/(x-2) lim as x approaches pi/4 (tan(x)-1)/(x-(pi/4)) Homework Equations equations above The Attempt at a Solution for the first limit, i tried substituting t = (pi/2)-(pi/x) but i got stuck i have no idea how to do the...

Homework Statement My question has two parts. The first part is the solution of the following integral: \int^{\infty}_{-\infty}\frac{cos\:x\:dx}{1+x^{2}} They give the answer as being \frac{\pi}{e} This is actually an example problem in the book, but I don't understand how...

Homework Statement Evaluate the integral of (1/Sqrt(5x-x^2)) Homework Equations [d/dx]{arcsin(x)}=(du/dx)/sqrt(1-x^2) The Attempt at a Solution arcsine(2x-5)/5 I did end up getting the right answer, but have no idea how I got there.

Homework Statement Find all the natural domain of the function algebraically, and confirm that your result is consistent with the graph produced by your graphing utility. h(x) = 3/2-cosx Homework Equations (a) h(x) = 3/2-cosx (b)x2-1/(x+1) The Attempt at a Solution Do I need to...