Trig Definition and 1000 Threads

Trig work problem... (am I correct?) Homework Statement If we call the height @ which the supports cross ,x, express this height as an equation in terms of H1 and H2 Only... Use similar triangle... Are my proportion correct? x/H1 = (L1-L)/L1 x/H2 = (L)/L1 = (L1-L)/L1 Because Where...

Homework Statement \int\frac{\sqrt{x^2 + 36}}{4x^2}}dx Homework Equations sqrt(a^2 + x^2) substitution for x = a tan theta The Attempt at a Solution I set x = 6 tan theta x^2 = 36 tan^2 theta dx = 6 sec^2 x \int\frac{\sqrt{36 + 36 tan \theta}}{144 tan \theta}dx \int\frac{\sqrt{36(tan...

Homework Statement Six Identical pipes, each with radius of 1 foot are ties tightly together with a metal band... Find the length of the metal band... I posted a picture... My strategy is dividing the figure in half Then finding the measure of the two arcs in red ( which should be...

Homework Statement y = 1/x - sin(x) What is the best strategy to graph this? I am having a difficult time drawing accurate graphs of these types of functions...

Ok... (2, -3) R = (Sqrt x^2 + y^2) R = (sqrt (2)^2 + (-3)^2) R= (sqrt 13)^2 R=13 Sin = y/r Sin -3 / 13 ? Cosin 2 / 13 ? But then.. how come the answer gives me sin -3 (sqrt13) / 13 and for cosin 2(sqrt13) / 13 My question is how come there's a (sqrt13) included for the...

Ok- I am teaching trigonometry to low level students right now and I am trying to figure out why they need to know the unit circle. Are there some interesting things they can learn about by using a unit circle? So far, we pretended it was a magic-barbie-sized-half-underground-ferris-wheel...

Homework Statement my professor tell me that when looking at the case ∫ √ (a^2 - x^2) , the trig substitution of course is asinϑ where -pi/2 ≤ ϑ ≤ pi/2. What I don't understand is why my professor tells me that when this term, √ (a^2 - x^2), is in the denomenator of the integrand that we must...

This is part of the derivation in EM theory. I try to simplify and be very specific. I don't agree with the book but this book usually is accurate: I need to find: cos (\frac {n\pi}{2} + \frac {n\pi x}{2}) \;\hbox { where }\; n= 1,3,5... The usual way to solve this is: cos (A+B) =...

I found one of the answers to the problem, and I took a peak, but couldn't find out how the book got the second answer. Problem- A batted baseball leaves the bat at an angle of θ with the horizontal and an initial velocity of v0=100 feet per second. The ball is caught by an outfielder 300...

I just want to know, what tan-1x means to you guys? does it mean arctan or cot? What about tan-2x? Isn't that cot2x? Shouldn't the notation tan-2x be banned to avoid misinterpreting it as an inverse trig function?

Homework Statement Problem 6. If you know that tan(theta) = -4/5 and sin(theta) > 0, find: (a) sin(theta) (b) cos(theta) (c) tan(theta + pi)Homework Equations cos^2(t)+sin^2(t)=1 tan(t)=sin(t)/cos(t) The Attempt at a Solution My teacher went over this today, but likes to skip over steps that I...

Homework Statement 3(sin(x)^4+cos(x)^4)-2(sin(x)^6+cos(x)^6)=1 (these are sinx raised to the 4 and 6 powers, not x^4or6) Homework Equations Pythagorean Identities The Attempt at a Solution I've tried using pythagorean identities to change everything to terms of sine or...

Homework Statement I was reading on the Weierstrass substitution, and I came across the following trigonometric identity: tan^{-1}(\alpha) - tan^{-1}(\beta) = tan^{-1}\left(\frac{\alpha-\beta}{1+\alpha \beta}\right)Homework Equations I'm not really sure which equations are applicable here...

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 Integral of 1/(2+sin(x)) dx Homework Equations The Attempt at a Solution I've been told that you can use trig subs, but I never had to learn that in high school and it hasn't appeared in any of my calculus coursework. As a side note. I've been wondering if it...

Homework Statement It's been a couple of years since I've done real math, so I'm kinda stuck on this one. This is actually part of a physics problem, not a math problem - but I'm stuck on the calculus part. I'm trying to solve this guy: \int \limits_{-\infty}^{\infty}...

Homework Statement find the volume of a sphere of radius R by integrating over the primary volume elements in cartesian coordinates. Hint: use a trig substitution for your integral over dy Homework Equations The Attempt at a Solution I don't understand what the problem wants me...

When formally proving trig identities using algebra are you allowed to divide? Ordinarily I wouldn't think twice about this. Sure, the trig function by which you are dividing might take on 0, but not for all angles. We divide by potential zeros all the time. My advisor was being very coy...

Homework Statement ∫ x/(x^2 + x+ 1)dx Homework Equations The Attempt at a Solution ∫ x/(x^2 + x+ 1)dx not really sure where to start on this one, i feel like i should factor the denominator in such a way that i have an expression whose derivative is some constant times x. help please

Homework Statement This is only a step in a bigger example problem on trig substitution 2/3 *x2 = sin2\theta \sqrt{}2/3 * x =sin\theta \theta = arcsin(\sqrt{}2/3 * x) and x = \sqrt{}3/2 * sin\theta This makes sense Then I saw dx / d\theta = \sqrt{}3/2 * cos\theta Uh... why...

Homework Statement sorry wait a few moments for the details, i hit post on accident prematurely ∫ √(1 + x^2)/x dx The Attempt at a Solution ∫ √(1 + x^2)/x dx x = tanϑ , dx sec^2ϑ dϑ -π/2 < ϑ < π/2 √(1 + x^2) = secϑ ∫ (secϑ * sec^2ϑ dϑ )/ tanϑ dϑ after using trig identities...

Homework Statement ∫ x^2√(a^2 - x^2) dx evaluate integral from 0 to a Homework Equations The Attempt at a Solution so i know the format of this problem requires the substitution of asinϑ -π/2 ≤ ϑ ≤ π/2 , but i don't know how to change the bounds of the integral...

Homework Statement rock rises straight upward frim the valley floor. From one point the angle of elevation of the top of the rock is 16.7 deg. From a point 168 m closer to the rock the angle of elevation of the top of the rock is 24.1 deg. How high is the rock... I added an attachment...

Homework Statement this is the first problem like this I've ever tried so take it easy!:redface: evaluate the integral I = ∫ x^3/√(16-x^2) dx from 0 to 2√3 The Attempt at a Solution - π/2 < ϑ < π/2 x = 4sinϑ , dx = 4cosϑdϑ *x = 2√3, x/4 = sinϑ , sinϑ = √3/2 , ϑ = π/3 x = 0 sinϑ = 0...

Homework Statement Find the partial derivative with respect to x of sin(xyz - 1) Homework Equations None needed. The Attempt at a Solution I took the answer to be yz*cos(xyz - 1), but wolfram alpha is giving me yz*cos(1 - xyz). Anyone know what's going on here? Thanks!

Homework Statement Find the exact value of each expression: a) sec-1(\sqrt{}2) b) sin-1(1) Homework Equations sec\theta=\stackrel{}{}1/cos\theta The Attempt at a Solution I've never learned this, but I am really curious in how it is solved. Is there a formula for this? Thanks!

Homework Statement I am having trouble row reducing... 5cos(t) 5sin(t) | -cos(t) 2cos(t)+sin(t) 2sin(t)-cos(t) | sin(t) Homework Equations The Attempt at a Solution I know I am allowed to multiply a row by a constant but I...

Hello! I'm having some trouble with finding the fundamental period of the slightly more complex trig functions. I think it's pretty simple stuff but I can't seem to crack it and I really need to get this bit sorted before I can move on with Fourier Expansions. I can do the more simple...

Homework Statement Solve for n: 2n.Cos^2(n)=1000 The Attempt at a Solution So, I think there's a substitution involved here. I tried to rearrange cosine in terms of sine to make it into a quadratic but that didn't work. I've gone through all the table trig identities. I've had other...

In the attached picture there is a right triangle (the right angle is on the right bottom corner). The angle, theta, is on the left-most side. From what i remember, sin (theta) is equal to opposite/hypotenuse. If you can see in the picture, it has written: delta x = h/sin(theta) so...

Homework Statement Integral of dx/[(x2 - 2x + 2)2]Homework Equations Trig substitution rules: for expression sqrt(a2 - x2) make x = asin(t) with -(pi/2) < t < (pi/2) for sqrt(x2 - a2) make x = asec(t) with 0< t < (pi/2) and for sqrt(a2 + x2) make x = atan(t) with -(pi/2) < t < (pi/2)The...

Homework Statement What is the importance of knowing how to express trig ratios in terms of sine, cosine, tan, cosec, sec, or cot? Homework Equations The Attempt at a Solution

Trig Question... Homework Statement Prove: cos/(1-tan) + sin/(1-cot) = sin + cos The Attempt at a Solution Cos/(1-sin/cos) + sin/(1 - cos/sin) cos/((cos-sin)/cos) + sin/ ((sin - cos)/sin) cos^2/(cos-sin) +sin^2/(sin-cos) (cos - sin)(cos+sin)/(cos - sin)^2 (cos + sin)/(cos...

Homework Statement I have been practicing proving trig. ident. for the past couple of days... although I am getting better... I wanted to ask are there any strategies that I should be aware of to make the process easier ? Homework Equations The Attempt at a Solution

\int x^{2} \sqrt{4+x^{2}} dx I've already subbed in: x = 2tan\theta dx = 2sec^{2}\theta d\theta and I've gotten down to: 16 \int tan^{3}\theta sec^{3}\theta d\theta But now I have noo idea what to do! Can someone give me a hint?

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 Find number of deg. subtendedat the center of a circle by an arc whose length is 357 times the radius,taking pi = 3.1416... The Attempt at a Solution The arc length is... 357(r) The radius length is r One revolution = 2r(pi) = arc lenght. Now I will solve...

Homework Statement The book states a proof... which says that the ratio of circumference/Diameter which this ratio is equal to pi which is the same for all circles... Ok that obviously make sense noting that circumference = Diameter(pi) which equals circumference/Diameter = pi My...

Homework Statement \int \frac{cos x}{sin^2(x) - sin(x)-6}2. The attempt at a solution I first tried factoring the denominator. \int \frac{cos x}{(sin(x) -3)(sin(x)+2)} The first thing that came to my mind was Partial Factoring but I don't think it would work in this case.Thanks in advance!

Problem Distance: From city A to city B, a plane flies 650 miles at a bearing of N 48° E. From city B to city C, the plane flies 810 miles at a bearing of S 65° E. Find the distance from A to C and the bearing from A to C. Work so far So far I've gotten the distance from A to C already...

Homework Statement Hey, I've been working through a book and one problem just gets me that I know should be a piece of cake. I don't know if I'm just being an idiot or not seeing something but the problem is to take int e^(ax)cos(bx)dx and int e^(ax)sin(bx)dx simultaneously by multiplying the...

Homework Statement I came across this interesting Trig problem that involves an angle θ formed by two rays OB and OA. there are two circles, one with radius a and one with radius b, on on the ray OA that are both tangent to one another. The ray OB is tangent to both of the circles. Show...

Homework Statement Evaluate the trigonometric expression (several examples). Hint: In each case, sketch a right triangle. For example, in the first case, sketch a right triangle with a hypotenuse of length 5 and one leg of length 3. Let A be the angle opposite the side of length 3. Solve...

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

Homework Statement Hello. I came across a question that required me to solve for invariant points between a base trig function and the function after horizontal stretch. I can't remember the exact question right now, but I'm just wondering how I would go about solving it if I didn't know...

Hi all. I have to solve this simultaneous trig equation and I am stumped. Can anybody give me a worked solution please? b*cos 30 = 1375*cos theta (i) b*sin 30 + 1375 sin theta = 1500 (ii) I end up with: b= 1375cos theta / cos 30 substituting into (ii) 1375 cos...

Homework Statement This is taken from a much larger problem, but I only need the answer to one particular question. Please help me understand why the height that a pendulum swings is r(1-cos\theta) where r is the length of the string and theta is the angle it swings through.Homework Equations...

Homework Statement Indefinite Integral (x^3)sqrt((x^2)+4)dx Homework Equations With an x= 2tan@ and dx= 2 (sec^2)@ d@ The Attempt at a Solution I get to 8(tan^3)@(sqrt((4tan^2)@+(8sec^2)@d@ Simplified down to 8(tan^3)@(sqrt((12tan^2)@+8d@ After that I'm stuck The...

Homework Statement tan 2x = 8cos^2 x - cot x. Solve where x 0 ≤ x ≤ pi/2 Homework Equations The basic trig identities The Attempt at a Solution I tried many different things which all eventually led to no solution. Firstly I tried solving the problem as I would a rational...

Homework Statement the problem is: tan(theta) = cos(theta) find theta: -pi < theta < pi Homework Equations tan(theta)=sin(theta)/cos(theta) sin^2(theta)+cos^2(theta)=1 The Attempt at a Solution