What is Trig: Definition and 1000 Discussions

I was stuck for an hour trying to do this calculus 1 problem. Think I figured it out but it's a even problm. Find the absolute maximum and absolute minimum values of f on the given interval. f(t)=t+cot (t/2), [pie/4,7pie/4] f'=1-(1/2) csc^2 (t/2) So 1=1/2*csc^2 (t/2) 2=csc^2...

Please forgive me as I may have to edit this post to get the equations to show properly. I am doing some work with AC circuits and part of one of my phasor equations has this in it: \frac {2i} {1+cos(θ) + i sin(θ)} - i , where i is the imaginary number \sqrt{-1}. However, knowing the...

Homework Statement 25∫5(sin(x))^3*cos(x)^2 dx Homework Equations 25∫5(sin(x))^3*cos(x)^2 dx The Attempt at a Solution 5(sin(x))^2 * sin(x) * (cos(x))^2 5(1-(cos(x))^2) * sin(x) * (cos(x))^2 25∫5((cos(x)^2)-(cos(x)^4))sin(x) dx Now I'm stuck.

\int \frac{81/100}{100x^2 + 81} so I know this is 1 + tan^2\theta but how do I implement it? isn't it a^2 + x so should i let x = 100tan\theta?

y = tan 3x, y = 2 sin 3x, −π/9 ≤ x ≤ π/9 It's looking for the area in blue there. Now obviously the -pi/9 to 0 is one region, then 0 to pi/9 is the other, but presumably you could find the area of one then double it (which is what I tried to do) but it wasn't right. The incorrect answer I...

I want to learn algebra II, trig and calc over the summer but I have a terrible time learning by reading, so is there some youtuber that does tutorials or a program like code academy except for math? Thanks!

Need to find derivative y = θ(sin(ln θ)) + cos(ln θ) My work θ(cos(ln θ))(1/θ) + sin(ln θ) + (-sin(ln θ)(1/θ)) (θcos(ln θ))/θ] + sin(ln θ) + ( (- sin(ln θ))/θ) cos(ln θ) + [θsin(ln θ) - sin(ln θ)]/ θ answer in book is 2cos(lnθ)

Homework Statement ∫cos(x)^5 / sqrt(sin(x))dx Homework Equations ∫cos(x)^5 / sqrt(sin(x))dx The Attempt at a Solution i tried to break up cos(x)^5 ∫(cos(x)^2)(cos(x)^3)dx I tried an identity (1-sin(x)^2)(sin(x)^-.5)cosx^3 I tried to distribute the sin(x)^.5 and use a...

How can we prove $$\displaystyle \tan^{-1}\left(\frac{4}{7}\right)+\tan^{-1}\left(\frac{4}{19}\right)+\tan^{-1}\left(\frac{4}{39}\right)+\tan^{-1}\left(\frac{4}{67}\right)+...\infty = \frac{\pi}{4}+\cot^{-1}(3)$$ My Trial: First we will calculate $\bf{n^{th}}$ terms of Given Series...

I just wanted to clear a couple of things up in terms of strict mathematical definition... Is the correct definition of the trigonometric ratios: cos\varphi=\frac{|x|}{r}, sin\varphi=\frac{|y|}{r} as opposed to: cos\varphi=\frac{x}{r}, sin\varphi=\frac{y}{r} (note the lack of...

Homework Statement The length of the curve r(t) = cos^3(t)j+sin^3(t)k, 0 =< t <= pi/2 is Homework Equations AL in polar = ∫sqrt(r^2 + [dr/dθ]^2) The Attempt at a Solution I am having trouble simplifying the terms within the square root. What method should I use to deal with...

\int_{0}^{a}\frac{x}{(x^2+z^2)^\frac{3}{2}}dx Hi all, I'm stuck on this one. Sure there's an easier way to do it. Don't have my calc book currently. Thanks!

Hey guys, I'm reading the Theory of Sound and I've come to a part in which I'm having trouble double-checking the algebra. Suppose we have two harmonic sound waves of equal amplitude traveling directly perpendicular to each other. \begin{align} u=acos(2πnt-ε) && v=bcos(2πnt) \end{align} They...

By using the averages of high and low tide levels. The depth of the water in a seaport can be approximated by the sinusoid d=3.2sin0.166pi(t-2.5)+14.1 where d is the depth and t is the hours after midnight. if a ship needs at least 12 m of water in a seaport to dock safely, how long could the...

I have no idea how to go about proving this trig identiy. I mean, I've been taught that it's a safe bet to convert everything to sines and cosines, but other than that, I've no clue. Am I even on the right path?

When would you use trig substitution vs. partial fractions? I know partial fractions is when you have a polynomial over a polynomial, but some of the problems in the trig substitution section in my book had polynomial over polynomial and used trig substitution?

Homework Statement Integrate dx/((x^2+1)^2) Homework Equations Tan^2=sec^2-1 The Attempt at a Solution So I let x=tanx then dx=sec^2x Then plugging everything in; Sec^2(x)/(tan^2+1)^2 So it's sec^2/(sec^2x)^2) which is sec^2x/sec^4x Canceling out the sec^2 gives...

Evaluation of $\displaystyle \int\sqrt\frac{1+\tan x}{\csc^2 x+\sqrt{\sec x}}dx$ I have Tried The Given Integral Using $\displaystyle \tan x = \frac{2\tan \frac{x}{2}}{1-\tan^2 \frac{x}{2}}$ and $\displaystyle \cos x = \frac{1-\tan^2 \frac{x}{2}}{1-\tan^2 \frac{x}{2}}$ and $\displaystyle \sin x...

I'm wondering if someone who is experienced can list all the content that a person should have mastered in the subjects of Algebra I/II and Precalculus and Trig. I completed College Algebra at community college just this past year and I'm going to be taking Precalc./Trig this upcoming year...

Please see question 9ii: Paper: http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202012%20-%20QP/6664_01_que_20120307.pdf Mark scheme: http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202012%20-%20MS/6664_01_msc_20120123.pdf This is my...

Homework Statement Prove cot(x) - tan(x) = 2tan(2x) Homework Equations Trig identities http://en.wikipedia.org/wiki/List_of_trigonometric_identities The Attempt at a Solution I have worked it down and don't think they are equal. I think it's supposed to be 2cot(2x) not 2tan(2x)...

Hi guys, This has caused me some confusion. Any help in this regard would be greatly appreciated. Homework Statement Given that \theta is an acute angle with sin\theta=19/51 find the exact value of cos\theta Homework Equations The Attempt at a Solution All I seem to be getting based on my...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Evaluate the integral. Homework Equations \int sin^2(\pi x) cos^5 (\pi x) dx The Attempt at a Solution I tried first by splitting the cosine up \int sin^2(x) [1-cos^2(x)] cos^2(x) cos(x) dx and from there use u-substitution. However, I am not sure what...

Homework Statement According to my math book, I solved the following trig equation correctly: 1) cos3x=0,500= 3x = 60° + n360° x=20+n120° 2)I also solved this problem correctly: 4sin^2x -3sin^x= 0 sinx(4sinx-3)=0 x=n*360° or 4sinx=3 sinx=3/4 x= ca. 49° x=49° + n360° or 131+ n360°. Now I´m...

Homework Statement ln(sec^-1(3x^2 +1)) Homework Equations The Attempt at a Solution 1/sec-1(3x2+1) * 1/(3x2+1)(sqrt(3x2+1)2-1) * 6x Is this correct ?, do I just simplify from here ?

Homework Statement show that sin4x + 2sin2x = 8sinxcos^3x Homework Equations sin2x =2sinxcosx The Attempt at a Solution I started out by letting sin4x = sin(2x*2) so that I could plugg in sin2x = 2sinxcosx in the equation. sin(2x*2) +2sin2x = sin2*sin2x +2sin2x = sin2 *...

If I understand my next possibilities in college, I think I can take either calculus 1 or trig 1, which do I take?

Homework Statement show that ((tanx - sinx)/sin^3x) = (1/(cosx - cos^2x)) Homework Equations sin^2 = 1-cos^2v cos^2 = 1-sin^2v The Attempt at a Solution On the left hand side: I plugged in sinx/cosx for tanx. I then divided both the numerator and denominator by sinx to get...

Homework Statement use trig identities to show that (b) cos(tan^(−1)[x])=1/√(1+x^2) for −1/2π<x<1/2π. Homework Equations i think Pythagoras has to applied but that is geometric reasoning hmm The Attempt at a Solution

Homework Statement Prove the formula xcscx=2B(ix)-B(2ix)Homework Equations B(x)=x/((ex)-1) sinx= (eix-e-ix)/2i The Attempt at a Solution I know that it makes sense to use the formula for B(x) with x=ix and x=2ix, and rewrite xcsc(x) as x/sin(x), plugging the above relevant equation in for...

Homework Statement Given u(x,t) = sum( e^(-at/2)*cos(n*pi*x/2L) * Re[A_n*e^(i*w_n*t)+B_n*e^(-i*w_n*t)], and the boundary conditions u(-L)=u(L)=0 for all t; du/dt = 0 for all x at t = 0; u(x,t=0) = e^(-|x|/l) Find A_n and B_n. Homework Equations N/A The Attempt at a Solution I have...

Hi MHB, Do you think this problem can be approached wisely, rather than expanding it and attack it using the Newton-Raphson method (which I did)? Problem: Solve $(\sec^4 x +16)^2=2^{12}(4\tan x+1)$ Thanks for reading and I would appreciate it if in case, you could solve it using shortcut...

so my given: s(t)=cos(pie8*t/4) took the derivative= velocity function then, v(t)= -pie/4 *sin(pie*t/4) When is the particle at rest? v(t)=0 now, 0= -pie/4 *sin(pie*t/4) im lost here. I know it's very simple I am just over thinking. What do I do from here? thanks

Why do trigonometric ratios have to be related to the angle between the base and hypotenuse of a right angle triangle? I am trying to understand why I can't use these ratios to any angle of a right angle triangle. I try to do that in the attached document. It seems to work for all ratios...

Okay so I'm working on this problem \int \frac{x^2}{\sqrt{4 - x^2}} \, dx I do a substitution and set x={\sqrt{4}}sinu I get to this step fine \int 4sin(u)^2 I know that u = arcsin(x/2) so I don't see why I can't just substitute in u into sin(u)? I tried this and I got \int 4 *...

A little confused on something. Suppose I have the integral 2 \int 4 \sin^2x \, dx So I understand that \sin^2x = \frac{1 - \cos2x}{2} BUT we have a 4 in front of it, so shouldn't we pull the 4 out in front of the integral to get: 8 \int \frac{1 - \cos 2x}{2} \, dx then pull out the...

Hi, I'm working on this problem: y = sin^2(x) / cos^2 (x) what is dy/dx? In the solutions it says to convert (sin(x)/cos(x))^2=tan^2(x) And the answer is dy/dx = 2sec^2(x)tanx However, using the quotient rule, I got this answer: dy/dx =[ (2sin(x)cos(x))cos^2(x) -...

Say we want to differentiate \arcsin x. To do this we put y=\arcsin x. Then x=\sin y \implies \frac{dx}{dy}= \cos y. Then we use the relation \sin^2 y + \cos^2 y = 1 \implies \cos y = \sqrt{1 - \sin^2 y} = \sqrt{1 - x^2}. Therefore \frac{dy}{dx} = \frac{1}{\sqrt{1 - x^2}}. My question is that...

Homework Statement Question is attached in this post.Homework Equations Question is attached in this post. The Attempt at a Solution I've solved the problem via using x=asinθ where a=1 I've been able to integrate the problem to the point where I get cos^2(θ)/sin^2(θ), but can't seem to...

Homework Statement Evaluate the integral x^(-1/5) tan(x^(4/5)) dx Homework Equations The Attempt at a Solution Set u = x^(4/5) Therefore du = 4/5 x ^ (-1/5) dx which gave me 5/4 ∫ tan(u) du integral of tan is natural log of absolute value of sec(u) sub in x^(4/5) for u...

I was testing for convergence of a series: ∑\frac{1}{n^2 -1} from n=3 to infinity I used the integral test, substituting n as 2sin(u) so here's the question: when using the trig substitution, I realized the upperbound, infinity, would fit inside the sine. Is it still possible to make...

My undergrad senior-year Mechanical Vibrations book tells me that I should remember the notion that Asin(θ+ø) can also be represented in the form of Bsinθ+Ccosθ (and other linear combinations of sines and cosines), from high-school trigonometry class. However, I was never taught this in my...

Homework Statement Sin(2x)=.98 Homework Equations I know you take arcsin of both sides and divide by 2 to get the answer which is 39, but where does this guy get 50 from? I would have assumed it occurred again at 2*39.. not 50. it is an online lecture. The Attempt at a Solution...

Im trying to determine the exact solutions (in degrees) to the trig equation shown below. I'm only interested in solutions over the interval [0, 360) . In my ti-83+, I input the function as y= 6(1/cos(X))^2*tan(X)-12tan(X). If I already know the number of solutions is 6, how can I tell this from...

Problem: Solve for t, 20 = 100 sin 2pi(50)t note: pi = "pie" I must be doing something wrong here. To solve algebraically, I first divide both sides by 100. Then, I get the inverse cosine of both sides, and set the angle in radians (.2013579208) equal to "2pi(50)t". Lastly I divide the derived...

Please note: I am in degrees I am remembering to include the restriction (|0<x<90) This is the only equation I've had trouble doing on my ti89 In order to solve a problem I am plugging in the following equations: 520cos(x) = 490cos(y) 490sin(y) + 520sin(x) = 678 Doing this by hand...

Homework Statement ∫8sin4x dx Homework Equations The Attempt at a Solution 8∫sin2xsin2x I'm not really sure what to do next. Maybe substitute a 1-cos2x in for one of the sin2x? Maybe both?

how do i go about integrating x*sqrt(1-x^4)?? i have no idea

how do u integrate sqrt(1 + x^2) / x?? i reduced this to sec^3(u)/tan(u) but how do i go from here??