Trigonometric Definition and 1000 Threads

Homework Statement Evaluate integral sqrt(x^2-9)/x dx Homework Equations The Attempt at a Solution I get this for my answer sqrt(x^2-9)+3sin^(-1)(3/x)+c which is apparently wrong because when I take the derivative of it I don't get the integrand my work is a attachment in this post wolfram...

Homework Statement Evaluate integral dx/sqrt(1-2x^2) Homework Equations The Attempt at a Solution My Answer: -cos^(-1)(sqrt(2)x)/sqrt(2) + c See my work in attachment Wolfram Alpha Answer: (sin^(-1)(sqrt(2) x))/sqrt(2)+constant...

Homework Statement Evaluate integral dx/sqrt(x^2-49) Homework Equations The Attempt at a Solution SEE POST #4 BELOW WITH ATTACHMENT TO VIEW MY SOLUTION EASIER TO READ i was trying to use a csc(theta) substitution and I don't see how my logic and math below is flawed but apparently I'm...

Evaluate integral sqrt(9-x^2)/x dx I get to here -3 ln|csc(sin^-1(x/2)+cot(sin^-1(x/3))|+3cos(sin^-1(x/3)+c I plugged in for theta because originally I had this -3 ln|csc(theta)+cot(theta)|+3cos(theta)+c and I set x equal to a expression x=3sin(theta) Hence i had to...

Homework Statement Evaluate integral csc(x)^4/cot(x)^2 dx Homework Equations The Attempt at a Solution Apparently I'm doing something wrong, what I'm not sure, thanks for any help My Answer: 2*tan(x) - (sec(x)^2*tan(x))/3 + c integral csc(x)^4/cot(x)^2 dx used fact that...

Homework Statement Evaluate integral sin^(-3/2)(x)cos^3(x) dx Homework Equations tan(x)=sin(x)/cos(x) sin^2(x)+cos^2(x)=1 sin^2(x)=(1-cos(x))/2 cos^2(x)=(1+cos(2x))/2 integral cos(x)dx = sin(x) + c integral sin(x)dx = -cos(x) + c d/dx sin(x) = cos(x) d/dx cos(x) = -sin(x) a^m/a^n=a^(m-n)...

Homework Statement Evaluate integral( sin^3(x) cos^5(x) ) dxHomework Equations sin^2(x) + cos^2(x) = 1 integral x^n dx = x^(n+1)/(n+1) + c d/dx cos(x) = -sin(x) a^n*a^m=a^(n+m) The Attempt at a Solution I got -cos^6(x)/6+cos^8(x)/8+c Apparently I did something wrong SEE ATTACHMENT Thank...

Homework Statement Apparently I'm doing something wrong. I'm kind of lost as to what because I looked over my work several times. Homework Equations sin^2 x = ( 1 - cos 2x )/2 cos^2 x = ( 1 - sin 2x )/2 integral sin(x) dx = -cos(x) integral cos(x) dx = sin(x) The Attempt at a...

Homework Statement This is a question from my test paper. If sec \theta=\frac{4xy}{(x+y)^2}, where x,y \in R, then (a)x,y \in R+ (b)x,y \in R- (c)x=y\neq0 (d)x\inR+, y\inR- Homework Equations The Attempt at a Solution I don't understand what i have to do and where should...

Homework Statement integrate xarctanx/(x^2 + 1)^2 Homework Equations Integration by parts possibly? I was attempting to do it without integration by parts because we went over this in tutorial and my TA couldn't solve it properly, hence why I'm here. The Attempt at a Solution I...

Homework Statement I understand that y = sin -1 x. However, why is it that when one writes x = sin y, one leaves out the -1 Homework Equations The Attempt at a Solution I know that when you invert a trig function, the dependent variable essentially switches from y to x and the...

Homework Statement Use 2 or more substitutions to find the following integrals hint : begin with u=cosx Homework Equations Integral 0--->pi/2 (cosxsinx)/swrt(cos2x+49 dx The Attempt at a Solution I'm still a little fuzzy on using multiple substitutions. From what I've read on...

I'm trying to figure out the steps required to do the following simplification: This equation: b/(a^2+ ω^2 )*(-a*sin(ω*t)+ω*cos(ω*t)) can be simplified to the following: (b/√(a^2+ ω^2 ))*sin(ω*t+ θ) θ= tan^(-1) (- ω/a) I can numerically verify that this is true but I am having...

Homework Statement Find the Derivative of: (ln(cos4x)) / 12x^2 Homework Equations y' ln(x) = 1/x The Attempt at a Solution I have determined the correct answer, but I am still confused as to how I came to the solution. Starting with the numerator, the derivative of cos...

Having Trouble: Solving a Trigonometric Equation using Identities ? Homework Statement I am having problems with these. Need some help please! Here is a sample question I am having troubles with: 3 cos θ + 3 = 2 sin^2 θ, 0 <= θ < 2pi I am really struggling with these. Any help...

Homework Statement \int(cosx)^5sin(x)dx, the question asks me to simply find the integral. Homework Equations cos^2(x) + sin^2(x) = 1 The Attempt at a Solution I have an odd power of cosine so I should split that up into [cos^2(x)]^2(sin(x)cos(x)), then I change cos^2(x) to...

I want a timeline for trigonometric function and how it was developed. Just like who created it and stuff like that. Did the greeks know about trigonometric functions? Is a tangent in calculus the same as a tangent in trigonometry and the function os a trigonometry? How do trigonometric...

Homework Statement A boat leaves the harbor going 60 degrees north-east with the speed 20km/h. 3 hours later, another boat leaves a harbor 160km to the east with a speed of 70km/h. What course should the second boat have to meet the first? Homework Equations Not 100% sure what equations would...

Homework Statement cos\theta/1-tan\theta+sin\theta/1-cot\theta=sin\theta+cos\theta Homework Equations The Attempt at a Solution

e.g. I want to find y when x is at pi/2 for the graph y=cos pi x. Why does pi/2 have to be expressed as a 'normal' (for want of better word) number (3.14/2) and not as 90 degrees (180/2) like you would for a graph without a pi in it e.g. cos x For cos x, if x is at pi/2, then I just put in...

Fx = sin [ 90 - theta ] * [ dX - [tan (theta) * dY ] ] ??

Hi, I was asked to solve for this: sin (2x) = sin (0.5x) For 0 to 270 degrees I know how to solve it by plotting the two graphs, is there any other way of doing it, like, for example, algebraically? Thanks, Peter G.

1. Hi, I have a pre-calculus final tomorrow, and there are a few questions I don't understand. I'd truly appreciate it if you could help :) 1. If sin(theta)=1/4, theta in quadrant II, find the exact value of cos(theta+pi/6) 2. sin(sin^-1(2/3) + cos^-1(1/3)) -- simplify 3...

Hi, 3sin(2x) = sin (x) I managed to find two answers: 80.4 Degrees and 279.6 degrees but I don't know hot to get 0, 180 and 360 as answers, can anyone help me? This is how I found the two other angles: 6 sin (x) * cos (x) = sin (x) cos (x) = sin (x) / 6 sin (x) cos (x) = 1/6 Thanks in...

Hi :smile: So, this is what I have to solve: 2sin2x - sin x = 0 I got two possibilities: sin x = 0.5 sin x = 0 From the second equation: I got 0 and 180, or, in other words, 0 and 3.14. The book has these two answers but the only other answer it has is 6.28 (and by the way, my domain is 0...

Hi :smile: A weight hangs on the end of an elastic string. The weight is pulled down and released from rest at time t = 0. The length x centimeters of the string at time t seconds is given by the formula: x = 7 - 2sin(πt) a) Sketch the graph of x against t for 0 <= x <=4 b) Find the two...

Homework Statement t = tetha FInd sin 2t when cos t = 4/5 Homework Equations no idea The Attempt at a Solution no. . . . btw what should I do 1st? I don't understand this question

So, in integrals that lead to inverse hyperbolics and can be solved with trigonometric substitution i just get lost. I know how to use both of them but i don't know which to use. For the sake of simplicity i'll just go with this one ∫ dx/sqrt(4+x^2) We know this equals arcsinh(x/2)...

Dear all, Homework Statement Draw behavior around (0,0) of solutions to the following nonlinear system \left( \begin{array}{c} x'(t) \\ y'(t) \end{array}\right) =\left( \begin{array}{cc} cos {x(t)} + sin {x(t)} + {x(t)}^2 + {x(t)}^2{y(t)}^3 \\ -x(t) + {y(t)}^2 + y(t) + sin {y(t)}...

Homework Statement For the angle shown a point is given on its terminal arm. Calculate the values of the three reciprocal trigonometric ratios, accurate to 4 decimal places if necessary. below is the link of the picture referring to the question https://www.virtualhigh...

Homework Statement I took a test in my Precalculus class about 3 weeks ago, and the tests were handed back this week. I saw that I didn't do so well because I was stumped on this equation: 3sinx + 4cosx = 1 Homework Equations We were to use the following formulas to solve this equation...

i have solved some questions but my answers don't match with the solution list i have in my book... please if you help me check my answers, i'll be very grateful.. √3 tan x - sec x - 1 = 0 ... i get three solutions to this question but my book's got two... it doesn't mention 5pi/3 + 2n*pi...

solve the trigonometric equations tan 2(theta) + cot(theta) = 0 When i solved this question, i got pi/2 + 2n*pi and 3*pi/2 + 2n*pi ... but my book says the answer should be pi/6 + n*pi and 5pi/6 + n*pi Is my answer wrong?? if so, then what's your solution.?

Homework Statement Find x base of triangle: 2 pieces, 8+12 opposite end: x angle: \Theta ; angle formed by triangle of 8 units and x : 2\Theta Homework Equations tan\Theta = opp/adj tan 2\Theta = 2tan/1-tan2 The Attempt at a Solution tan\Theta= x/20 tan 2\Theta = x/8...

Homework Statement Solve the contour integral \int_{\gamma}\frac{2+z}{1-cos\left(z\right)}dz along a counter-clockwise circle of radius 1 centered at z=6 Homework Equations Cauchy's integral formula f\left(z\right)=\frac{1}{i*2\pi}\int_{\gamma}\frac{f\left(w\right)}{w-z}dw The...

Homework Statement Find all solutions to the following equation: sin((5*x/2)+15)=0.433 where 0 < x < 360 Homework Equations The Attempt at a Solution i can find the first value of x that satisfies this equation. (5*x/2)+15=sin^-1(0.433) 5*x/2=10.6581 5*x=21.2162 x=4.2632...

\intop_{-\pi/2}^{+\pi/2}\sqrt{(-6sin2t)^2+\sqrt{6}(cost)^2}dt how to solve it? i tried by parts and it looks very bad and complicated edit sorry i copied the wrond integral now it fine

\int \frac{\cos^2 x}{(1+\epsilon\cos x)^3}\,dx Where, \epsilon > 0 is a real number constant.

Homework Statement TanΘ = 4/3 pi < Θ < 3pi/2 Find... a.) Sin(2Θ) b.) cos(2Θ) c.) Sin Θ/2 d.) Cos Θ/s The Attempt at a Solution So... The line will be in quadrant III. Would sin = 4 and cos = 3? What I used for a.) is ... a.) Sin(2Θ) = 2sinΘcosΘ =...

I'm on mobile so I can't use latex.. sin^2 theta - cos^2 theta is not the same thing as one? If I had a problem say... 1 + cos^2 theta would that equal to sin^2 theta? Or -sin^2 theta? Thanks

Homework Statement 2.) Solve x7=1 I am to solve for all the solutions to this polynomial, including the complex solutions using trigonometry. I'm supposed to plot my solutions on the unit circle, with the x-axis being the real axis, and the y-axis being the imaginary (or complex) axis...

Homework Statement Tan \Theta = 12 / 5, sin\Theta<0Homework Equations Sin ^{2} \Theta+ Cos ^{2}\Theta = 1 The Attempt at a Solution Sin is less than 0 so... it should be somwhere in the II or III quadrant? What identities should I use to solve?

Homework Statement This problem came up while solving a physics problem in waves. We have the equation cos(96πt)cos(4πt)=0 How many times does the L.H.S. become 0 during the time t=0 to t=1s ? The Attempt at a Solution Nothing.

This is more of a trig question but its coming out of an integration problem I am dealing with... the initial problem is... \int\frac{\sqrt(1+x^2)}{x}dx I've worked through the problem with the book and down the line I have to integrate csc(theta) without using a handy-dandy table...

Homework Statement sec 3\Theta = 2 Find all solutions within 0 < \Theta < 2\Pi Homework Equations none The Attempt at a Solution I am having trouble "knowing" what angles satisfy sec = 2 within the interval. I can find one... ArcCos 1/2 = 1.047... which I can guess is...

a*sin(x)=b*sin(th)+c*sin(y) d+a*cos(x)=b*cos(th)+c*cos(y) Find x and y if all others are constants. I don't get how to solve this system of trigonometric equations in matlab. Please help me out friends. Thanks in advance.

Homework Statement Prove: lim (n→0) {(sin n cos n) / (ⁿ√(1 - tan² 2n + tan⁴ 2n - tan⁶ 2n + ...))} = 1Homework Equations The Attempt at a Solution The denominator is an infinite geometric series, using the sum formula of an infinite geometric series, I simplify the limit: lim (n→0) {(sin n cos...

Homework Statement Find the limit as x approaches 0 of xsin(1/(x^2)) Homework Equations The Attempt at a Solution I think this goes to 0, because the sine component just oscillates between 1 and -1, and gets multiplied by 0, for all x. I don't know how to show this using limit...

Homework Statement Prove http://img847.imageshack.us/img847/9428/trig.png Uploaded with ImageShack.us Homework Equations I am not quite sure how to prove this, I can see it involves using a double angle formula (see http://mathworld.wolfram.com/Double-AngleFormulas.html)...

I am not quite sure how to prove this, I can see it involves using a double angle formula (see http://mathworld.wolfram.com/Double-AngleFormulas.html). I have tried working backwards but to no avail. Any ideas? http://img847.imageshack.us/img847/9428/trig.png Uploaded with...