What is Trig: Definition and 1000 Discussions

Evaluate the integral \int \frac{x}{(x^2 - 4) \sqrt{x^4 - 8x^2}} \, dx by making the substitution u = x^{2}Homework EquationsThe Attempt at a Solutionu = x^{2} - 4 so \frac{du}{2}= xdx \int \frac{1}{(x^2 - 4) \sqrt{x^4 - 8x^2}} \, xdx \frac{1}{2} \int \frac{1}{(u) \sqrt{x^4 - 8x^2}} \...

Homework Statement A block with mass M is held statically on an overhang by a force Mg applied horizontally and the force of friction on the overhang. What are the normal and frictional forces? For what angles θ does the block remain at rest? The Attempt at a Solution In the picture...

∫[6x^6 sin (9x)]/[1+x^10] * dx I've set u =x^6 du=6x^5*dx dx=du/6x^5 ∫[6x^6 sin (9x)]/[1+x^10] * (du/6x^5) = ∫[x*sin(9x)*du]/1+x^10. Can someone help me figure out the next step? I'm thinking of putting a constant out in front, so I can use 2du for (x^10)

1.) ∫[(7 sin (x))/[1+cos^2(x)]] * dx 2.) I'm looking at the trig identity sin^2 x+cos^2 x=1, and am wondering if I could use that in solving the problem. Or should I use u=sin x, then du= cos x, then plug those in? 3.) so I thought maybe it would be easier to separate the two...

Homework Statement List all x-intercepts for y= -5sin(4x+pi/3) On the interval [-pi/6, pi/2) Homework Equations I know that y=sin has x-intercepts at 0, pi, and 2pi on the interval of [0, 2pi] but when I try to solve it the same way here it doesn't really come out the same...

Prove the identities $$ \frac{\sin\left(\frac{n + 1}{2}\theta\right)}{\sin\frac{\theta}{2}}\cos\frac{n}{2}\theta = \frac{1}{2} + \frac{\sin\left(n + \frac{1}{2}\right)\theta}{2\sin\frac{\theta}{2}} $$ By using the identity $\sin\alpha + beta$, I was able to obtain the $1/2$ but now I am not to...

Homework Statement \lim_{x\rightarrow \frac{\pi}{2}} \frac{tan(2x)}{x - \frac{\pi}{2}} Homework Equations The Attempt at a Solution I was given a couple of hints: use substitution, and that there isn't any need for the tangent double angle formula. I would have never thought to use...

Homework Statement Folks Evaluate ##B_{11}## given ##\displaystyle B_{ij}=\int_0^1 (1+x) \frac{d \phi_i}{dx} \frac{ d\phi_j}{dx} dx## where ##\phi_i= sin i \pi x## and ##\phi_j=sin j \pi x## Homework Equations The Attempt at a Solution I calculate ##\displaystyle B_{ij}=\int_0^1...

I have $h = 1+0.6 \cos \left( \frac{\pi t}{2}\right)$ and need to find where $h=1.5$ for $t\in [0,4]$ The period of the function is 4 and I get solutions of $\displaystyle 1.5 = 1+0.6 \cos \left( \frac{\pi t}{2}\right)$ $\displaystyle0.5 = 0.6 \cos \left( \frac{\pi t}{2}\right)$...

Homework Statement The two vectors a and b lie in the xy plane and make angles α and β with the x axis. a)By evaluating a • b in two ways (Namely a •b = abcos(θ) and a • b = a1b1+a2b2) prove the well-known trig identity cos(α-β)=cos(α)cos(β)+sin(α)sin(β) b)By similarly evaluating...

Homework Statement Simplify the following: (1/cos2θ) - (1/cot2θ)Homework Equations Various trig identities The Attempt at a Solution I tried to make cos2θ into 1-sin2θ and cot2θ into csc2θ-1 but still couldn't find any obvious solution. Help?

Why are reference angles necessary in trigonometry. I understand they are the acute version of an obtuse angle.

Show that: 4(\sin^4x+\cos^4x) \equiv \cos4x + 3. Really stuck with this, no idea how to go ahead with it. The book gives a hint: \sin ^4 x = (\sin ^2 x)^2 and use \cos 2x = 1 - 2\sin ^2 x But I don't even understand the hint, where did they get \cos 2x = 1 - 2\sin ^2 x from?

Homework Statement Solve this equation: cos^2(2x)=0,36 For x \in [-\pi;\pi]Homework Equations - The Attempt at a Solutioncos^2(2x)=0,36 \Leftrightarrow cos(2x)=\sqrt{0,36} \Leftrightarrow 2x=cos^{-1}(\sqrt{0,36}) And then I am not sure exactly how to proceed... When should I put in the...

I'm just curious on how to find out what quadrant θ is in from the information. I know it says that theta is obtuse, but doesn't this only conclude that theta is not in the first quadrant? In the solutions they have right away said theta is obtuse therefore it is in the second quadrant so k is <...

Solve for values of θ in the interval 0 ≤ θ ≤ 360, 2sinθ = cosecθ now if I do: 2sinθ = 1/(sinθ) and multiply by sinθ I can solve sinθ = ±√(1/2) but if I solve 2sinθ - 1/(sinθ) = 0 and factorise to get sinθ(2 - (1/sin^2θ)) = 0 I get sinθ = 0 which gives me more solutions then...

Prove: \frac{CosθSinθ}{1 + Tanθ} = Cos2θ =========================== I multiply out the denominator to get: CosθSinθ = Cos2θ + CosθSinθ I cannot seem to prove it. Starting to think it's a trick question.. :/

1 + 1 = 2 sec2x ______ ________ 1+sinx 1-sinx PLEASE SOMEONE HELP! UGH! In case you can't tell what that says, it's 1/1+sinx + 1/1-sinx = 2sec2x​

Homework Statement How do I find out the exact value of tan^-1 (1 / sqrt(3))? Homework Equations nada The Attempt at a Solution I don't know where to start.

Hello, Say I'm working with ∫ sqrt(1-cos(t)) dt I end up with a substitution of u = 1-cos(t) and dt = du/sin(t) sub back in: ∫ sqrt(u) / sin(t) du Still got a t in there ... hrrmmm So I go to wolfram alpha for some inspiration and 'show steps'...

Hey, I have the DE y'' -2y' + 3y = xsin(x) + 2cosh(2x) Using the D operator as D = \frac{dy}{dx} this becomes (D2 -2D +3)y = xsin(x) + 2cosh(2x) so yp = \frac{1}{p(D^2)} operating on xsin(x) + 2cosh(2x) (i think) So i know if this was say \frac{1}{p(D^2)} operating on...

I need to verify the given identity. I've tried every which way i can think of, but can't figure this one out. I am self-studying this book "College Trigonometry 5th Edition by Aufmann. This is exercise set 3.3, problem 63. cos^2(x) - 2sin^2(x)cos^2(x) - sin^2(x) + 2sin^4(x) = cos^2(2x)...

hi everyone, im currently trying to teach myself the D operator technique, as opposed to the 'guess method' which i don't really like. I stumbled upon this on yahoo answers: (D^2 + 1)y = 4 cos x - sin x Find the complementary function by solving the auxiliary equation: m² + 1 = 0...

Are you expected to know all of the trig formulas for the math gre subject test? I don't mean the easy ones, i mean ones such as the sum-to-product or product-to-sum. thanks!

Homework Statement See below. 2. The attempt at a solution Hey there, apologies for doing so, but I don't know how to use latex on this board (it doesn't show me anything when I hit preview, so I had to make a picture for the sake of cleanness. imgur.com/WzrAR.png The first line is the...

$\displaystyle (3)\;\; \int \frac{1}{\sqrt{1-x^4}}dx$

For example: tan(pi/2 - pi/4) = (tan(pi/2) - tan(pi/4) ) / 1 + tan(pi/2)tan(pi/4) Which of course comes out to: undefined + 1 / 1 + undefined Does that equal 1, or equal Undefined/No Solution?sorry for the poor formatting, I couldn't find the mathprint symbols for pi and fractions

Homework Statement The terminal side of angle θ in standard position lies on the given line in the given quadrant. Find sin θ, cos θ, and tan θ. Homework Equations 3x + 7y = 0; quadrant III The Attempt at a Solution The line does not go through the third quadrant. The course...

Why is that in high school, Trignometry is often not a course, but in college, it is? I remember in high school, after taking Geometry in Freshmen year, I took Algebra 2 in sophomore year. Then in junior year, i took Pre Cal, and then Calculus. I just took a placement test at a community...

1. Find the derivative of the function using the power rule or product rule 2. sinθ/2 + c/θ 3. I tried to do plus or minus the √1-cosθ/2

Homework Statement Determine the following and state quadrant. cos(-65°) Homework Equations I make this the 2nd quadrant. The Attempt at a Solution where:- -cos(180 - θ) -cos ( 180 - (-65)) -cos245 = 0.423 however i wasnt sure if it lied in the 4th quadrant...

Homework Statement Prove the identity. Homework Equations http://postimage.org/image/vjhwki1ax/ The Attempt at a Solution http://s13.postimage.org/jkhubi4lz/DSC03534.jpg

for derivative sinx = cosx, by setting up into formal definition formula limΔx->0 \frac{f(x+Δx)-f(x)}{Δx} this formal definition of derivative is formulated from the cartesian coordinate system where the horizontal is x and verticle is y. But sinx is a trig function and trig functions...

Homework Statement lim x-->0 sin(pi/x) sqrt(x^3+x^2) The Attempt at a Solution I was having trouble evaluating the above limit. Do I start by isolating x? For some reason, when it comes to trig functions such as this, I'm not sure how to simplify it. Also, what material would I have to...

Homework Statement Finding the derivative of x^2 sin x tan x. I need to simplify this: x^2 sin x sec^2 x + x^2 tan x cos x + 2x sin x tan x to: x (x sec(x) tan(x) + sin(x) * (x+2 tan(x))) Homework Equations Just what you see above.The Attempt at a Solution I can get it simplified to x(sin...

Homework Statement This isn't really a problem that was assigned to me, (I'm studying independently) I just have a question about the general concept behind some identities. Homework Equations sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b) sin(theta) = sin(180-theta) The...

Evaluate: 1. $\displaystyle \int_0^{\displaystyle 2\pi} \frac{x \sin^{2n}(x)}{\sin^{2n}(x)+\cos^{2n}(x)}dx$, $n>0$ 2. $\displaystyle \int_0^{ \displaystyle \pi \over \displaystyle 2} \frac{x \sin x \cos x}{\sin^{4}(x)+\cos^{4}(x)}dx$

I look for trig identitiy to simplify this expression: \frac{\sin(nx/2)}{\sin(x/2)} is there one specficic to use, or is there other ones that will help to simplifiy? I have been trying but can't make it simplier! Thanks!

Given Info: 4 m/s [N30°E] and 5 m/s [S17°E]. FIND: The Resultant Vector And it's angle.So I'm having a big problem with figuring the angles between the two vectors... I feel like I'm doing it correctly, but at the same time I'm not sure... Here's my diagram. http://i47.tinypic.com/x38osl.jpg So...

A 600 lb. wheel is set on a ramp inclined 30 degrees. What is the force required to keep the wheel from rolling down the ramp? I set the problem like this: And I thought the side labeled 'x' is the force needed to keep the wheel up there, which, if calculated by sin(3) = 600/x is 1,200 lbs...

Here is what I got so far: But the solution 15.7875 MPH is incorrect so undoubtedly my angle would come out incorrect too. Where have I gone wrong?

I know you can derive the double angle formulas for sin(2a) and cos(2a) from Euler's identity, but is there any way to derive the tan(2a) in a similar manner from an easier formula? What about the addition/subtraction formulas (i.e. sin(a+b), etc.)

I have to simplify (or get it in terms of tan I guess?) \cot (\frac{2\pi }{3} - x) I'm not sure how to get the reference angle and subtract the angle 'x' from it to get an expressional value...how would I do this?

I tend to forget some of the trigonometric functions and someone showed me how to derive the double angle identities from what I think is Euler's formula: e^{ix} = \cos x + i\sin x = e^{i2x} = \cos 2x + i\sin 2x = (e^{ix})^{2} = (\cos x + i\sin x)^{2} I have a question about this step...I...

Homework Statement I was working on a problem set involving greens theorem and I came across this peculiar trig substitution. I was just wondering how it came about as I couldn't find anything like it on Wikipedia's page. sin^4(t)cos^2(t) + cos^4(t) sin^2(t) = cos^2(t)sin^2(t) The...

i have try to intergral cos^2( x)/sinx. When i used sinx=t i got {[(1-t^2)^n-(1/2)]\t}. When i use intergral by parts i got {cos^2n-1(x)[1-cos^2(x)]} to intergral. If you could give me a tip to intergral this i would bn thankful to you!

Homework Statement Now, I know there's two ways to go about this and it seems everywhere I look around on the web people are solving it in a way I think that seems longer, harder and more prone to mistakes in exams. It involves using the exponential identities and taking logs. I was shown...

I struggled in adv alg 2 with trig my jr year. Some of it may have been me not applyling myslef this year. I passed with a C- (77%). How bad is that? And for my senior year I am going to take adv precalculus. People say its a review of alg 2. Is that true? I think the thing i struggle with most...

If $A+B+C=\pi$. Then Minimum value of $\cot^2(A)+\cot^2(B)+\cos^2(C)$ is

Homework Statement 244.10746 = 845.9064sin(θ) - 274.87cos(θ) Homework Equations Is there? I have no clue. The Attempt at a Solution I plugged it into WolframAlpha and I got an incomprehensible answer.