Trigonometric Definition and 1000 Threads

$$ \cos[k_n(L-\varepsilon)]-\cos k_nL $$ I just read this for small epsilon this result can be further simplied by using the trigonometric identity for $\cos[k_n(L-\varepsilon)]$. Doing so result is $$ 2\sin k_nL $$ I don't see this? Can someone explain?

solve for tan^4x + tan^2x = sec ^4x - sec^2x i solved and ended up with RIHS= tan^4x?

1. Homework Statement - multiplication of trigonometric function and complex exponential 2. Homework Equations the question is, Akcos(ωt) × e-jωt 3. The Attempt at a Solution it is, Ak/2 + (Ak/2)e-j2ωt ? by using cos(ωt) = 1/2ejωt + 1/2e-jωt

Homework Statement Hi I need help with the following integral. \int_0^2 \! \frac{1}{(x^2+4)} \, dx Homework Equations I believe that these are both trigonometric substitutions. However, these are the simplest in my textbook and I can't even understand them. :-( The Attempt at a Solution...

Homework Statement Prove the Identity sinθ/(1+cosθ) = 1-cos(θ)/sinθ Homework Equations sinθ/cosθ = tanθ sin^2θ + cos^2θ = 1 The Attempt at a Solution sinθ/(1 + cosθ) = LS cosθtanθ/(1+cosθ) = LS cosθtanθ/(sin^2θ + cos^2θ + cosθ) = LS cosθtanθ/(tan^2θcos^2θ +...

http://www.mathhelpboards.com/f12/im-clueless-how-start-2322/My math class uses an online homework system. I got the answer wrong to the question, but I can get a similar question. Here is one that is similar to the earlier one. You have two functions that are graphed. y=\frac{\csc^2{x}}{4}...

I have this as part of a calculus problem. I guess I am a little rusty on this. Any help would be appreciated. 4\cos^2{x}=\frac{\sec^2{x}}{4} I believe that I need to solve for cosx. And then determine what cosx is in radians. That should be the lower limit of the integration. I know how it...

How can we say: f(x)=A'sin(kx)+B'cos(kx) or equivalently f(x)=Ae^{ikx}+Be^{-ikx}?? How are these two equivalent knowing that e^{ix}=cosx+isinx I don't get this?

Homework Statement evaluate the given trigonometric integral ∫1/(cos(θ)+2sin(θ)+3) dθ where the lower limit is 0 and the upper limit is 2π Homework Equations z = e^(iθ) cosθ = (z+(z)^-1)/2 sinθ = (z-(z)^-1)/2i dθ = dz/iz The Attempt at a Solution after I substitute and...

Homework Statement Find the limit of the series \lim_{n \rightarrow \infty} \sum_{i=1}^{n} cos (i \theta / n) , 0≤θ≤π/2 Homework Equations The Attempt at a Solution I know that the expansion looks like \cos \theta / n + cos 2 \theta / n + ... + cos \theta , but I couldn't begin...

Hello everyone! Homework Statement Solving a relatively general equation representing a constant combination of 2 trigonometric functions.Homework Equations a\cos{(vx+p)}+b\cos{(ux+q)}=cThe Attempt at a Solution I really don't have any idea for a general solution to this equation.. Best Regards

Homework Statement A satellite follows a path that may be modeled by the function H(t)= 350 sin 28∏(t-25) + 400 Time is measured in days. Homework Equations The Attempt at a Solution A) Determine the period of the satellite: 2∏*1/28∏ = 1/14 days B) How many minutes will it...

Homework Statement Homework Equations Any trig formulas The Attempt at a Solution The yellow paper is me switching everything to sin and cos to see if that helps but it doesn't. I'm completely stuck here.

Homework Statement All solutions in the interval 0 ≤ x < 2∏ Sin 2x = -2cos x The Attempt at a Solution I went about it in two different ways. The first way: I simply used the double angle formula to get 2sinx cosx + 2cos x = 0 From this we get that whatever makes cos x = 0...

Homework Statement A beach ball is riding the the waves near Tofino, BC. The ball goes up and down with the waves according to the formula h= 1.4 sin(∏t/3), where h is the height in meters above sea level, and t is the time in seconds. A) In the first 10s when is the ball @ sea level. B)...

Was just double checking if we can simplify this in the following way, ∫ sinx * √(1 + cos2x) dx = ∫ sinx * (1 + cosx) dx

Does ##(\sin^{-1}\theta)^2 =\sin^{-2}\theta## ?

∫cos^5 x sin^5 x dx I thought I would try to solve this by first doing: ∫(1 - sin^2 x) cos^3 x sin^5 x dx but would like to know if that's right. [Edit] Is the answer something like (sin^6 x) / 6 - (sin^8 x) / 4 + (sin^10 x) / 10 ?[Edit]

Find ∫from .6 to 0 x^2/ sqrt(9-25x^2) dx My teacher worked this on the board a little confused O obviously the trig sub is asintheta. But it isn't in the right form yet. So get it there you pull out a 25 --) sqrt(25(9/25) - x^2 ) 5sqrt((9/25)-x^2 so x= (3/5) sintheta so dx = 3/5costheta. so...

Determine the signs of the trigonometric functions of the angle -200° in standard position. sin(-200°) cos(-200°) tan(-200°) csc(-200°) sec(-200°) cot(-200°) Information: Q1= (All Positive) Q2= (sin csc) Q3= (tan cot) Q4= (cos sec) Answer: sin(-200°) = Positive cos(-200°) =...

Find the values of the six trigonometric functions of an angle θ in standard position whose terminal side is containing the points (-3,0) Sinθ= Cosθ= Tanθ= Cscθ= Secθ= Cotθ= I believe the following are correct But I am not sure, Please give insight Sinθ= 0/3 Cosθ= -3/3 Tanθ= 0/3...

Does anyone know of websites where I can find many problems on the topic in the title line (my textbook has far too few)? Thanks!

Homework Statement The instantaneous value of current, i amp, at t seconds is given by: i = 15 sin(100π.t + 0.6) Find the value of; a) amplitude b) period c) frequency d) initial phase angel e) value of i when t = 2.5s f) time when current first reaches maximum value Homework...

Hi, I had to solve without the aid of a calculator: 2cos(x) = sin(2x) What I did was perform the following substitution: 2cos(x) = 2sin(x)cos(x) I then canceled and got: sin (x) = 1 For 0 to 3pi, I got two answers, pi/2 and 5pi/2. I did not get one of the answers. Why...

Homework Statement A ship is d feet from a dock (horizontal distance). The dock is 40 feet above sea level. The angle of depression from the dock to the ship is θ. Write θ as a function of d. Homework Equations This question is accompanied with choices. The choices are (A) θ = 40arctan(d) (B)...

Homework Statement Find the solution set of each of the following equations for the interval 0° ≤ x ≤ 360°. sin^2x = sinx Homework Equations Trigonometric Identities for Sine. The Attempt at a Solution This is my attempt so far: \sin^2x = sinx \sin^2x - sinx = 0 \sin^2x - sinx + \frac{1}{4}...

Homework Statement Given y = 2/3(arctan \frac{x}{4}), find x. Homework Equations Inverse trigonometric identities for tan. (I guess)The Attempt at a Solution I never attempted because it seems impossible for me. You think this is possible? Thank you!

Is this identity possible? cot 2x = \frac{cos3x + cosx}{sin 3x + sinx} Thanks!

Homework Statement Find the solution set of the equation below for the interval 0° ≤ x ≤ 360°: arccos(x) - arcsin(1-x) = 90° Homework Equations all given above. The Attempt at a Solution i tried to consider (1-x) as "complementary" but I'm not really sure about that and I would...

Homework Statement Verify that \frac{cosθ}{1-tanθ} + \frac{sinθ}{1-cotθ} = sinθ + cosθ is an identity.Homework Equations - Reciprocal Trigonometric Identities - Pythagorean Trig IdentitiesThe Attempt at a Solution Every time I try to manipulate the LHS of the equation I always get -1 and as far...

Homework Statement Prove that sin6 + cos6 = 1 - 3sin2cos2 Homework Equations (1) The Attempt at a Solution I tried to convert those all in terms of sine and cosine only but it didn't work.

EDIT: 1.Homework Statement The problem asks to simplify this: cos(arcsin x)Homework Equations let arc sin x = θThe Attempt at a Solution EDIT: I have to edit because I received a warning for not posting for #3 and #2. I originally posted "cos(arcsin x)" for #2 because that was what I know...

Homework Statement find the limit as x approaches 0 of 3sin4x / sin3x Homework Equations sin2x = 2sinxcosx lim as x ->0 of sinx / x =1 The Attempt at a Solution sin4x = 2 sin2x cos2x

Homework Statement Prove that: (1-tanθ)/(1+tanθ)=(cotθ-1)/(cotθ+1) Homework Equations Trig Identities: tanθ= sinθ/cosθ cotθ= cosθ/sinθ 1+tanθ=secθ 1+cotθ=cosecθ The Attempt at a Solution These sorts of equations are coming up a lot and I am having trouble understanding...

The question asks to find ∫secxtan2x I rewrote tan2x as (sec2x-1). Then I expanded the equation having sec3x-secx and I know the integral of secx which is 0.5ln|tanx+secx|, but my question is, is integrating sec3x by parts the correct path? or not? Thanks

The problem is to find \int(cos5x)/(\sqrt{sinx}) I rewrote cos5x as cosx(1-sin2x)2, finally getting: (cosx-2cosxsin2x+cosxsin4x)/\sqrt{sinx} and I don't even know if this is the correct path, so, any advice would be appreciated.

Homework Statement Simplify the following: sin(b)/cos(b) + cos(b)/sin(b) Homework Equations Trigonometric identities The Attempt at a Solution Ok so i have no clue how to do this,I keep trying but can't seem to get the right answer, I have tried to do this: sin(b)/cos(b) +...

[b]1. The problem statement: QUESTION:the general solution of equation (√3 - 1)sin∅+(√3 + 1)c0s∅=2 is 1) ∅=2nπ+- (π/4)+(π/12) 2) ∅= nπ + (-1)^π (π/4)+(π/12) 3) ∅=2(n+1)π (π/4)+(π/12) The Attempt at a Solution ACTUALLY I DONT NEED THE ATTEMPT, i know the answer is option 1 , i don't...

I have some questions and doubts in trigonometry. I hope somebody can solve these questions. Q1) If for real values of x, cos\theta = x +\frac{1}{x}, then a) \theta is acute angle b) \theta is right angle c) \theta is an obtuse angle d) no value of \theta is possible I will post the following...

Number of real solution of the equation $\sin (\sin (\sin x)) = \cos (\cos (\cos x))$ where $ 0 \leq x\leq 2\pi$

Spending my summer studying on my own, and I have come across some things which I would like to see how they are solved. If you are capable of completing, please show work instead of just answers so that I can follow what you did, and take notes on it. Homework Statement If sin(θ) =...

Homework Statement To prove that \sum over m=1 to 15 of sin(4m-2) = 1/4sin2, where all angles are in degress Homework Equations The Attempt at a Solution Tried to solve it using identity sinx+siny=2sin((x+y)/2)cos((x-y)/2)..but all attempts failed..help

Homework Statement Prove that limh→0[(cos(h-1))/h]=0. Homework Equations Half angle formula From an example: limh→0[(cos(h-1))/h] = limh→0[-(2sin2(h/2))/h] They state that they use the half-angle formula in the following way: cosh= 1-2sin2(h/2) I'm not really sure how they are getting...

Hello again, I have a question about a trigonometric substitution problem that I am struggling with. I was able to get the correct answer, which I know is correct because of Wolfram verification, and my school has a way of showing an example which showed the steps... Anyway, see below...

Homework Statement The problem along with its solution is attached as ProblemSolution.jpg. Homework Equations Δx = λ/sinθ (Eq. 1) Δp_x = (h/λ)(sinε) (Eq. 2) The Attempt at a Solution In Wikipedia, I found this article: http://en.wikipedia.org/wiki/Heisenberg's_microscope which uses...

Homework Statement ∫sin^3xcos^63xdx Homework Equations The Attempt at a Solution ∫sin^3xcos^63xdxsin^3xcos^63xdx let u=cosx du=-sinxdx -du=sinxdx =∫sin^2xcos^63xsinxdx =∫(1-cos^2x)cos^63x-du =-∫(1-u^2)u^63du =-∫(u^63-u^65)du =-u^64/64-u^66/66+c...

Hello again. I am hoping that someone can assist in checking my work regarding a trigonometric integral. The problem and my attempt to solve is as follows. \int\sin^{\frac{-3}{2}}(x)*cos^3(x) dx \int\sin^{\frac{-3}{2}}(x)*cos^2(x)*cos(x) dx Using a Pythagorean identity...

Homework Statement Show that : 1 + cos(2∏/5)= 2 cos(∏/5) Homework Equations cos(2x) = cos^2(x)-sin^2(x) cos^2(x)+sin^2(x) = 1 The Attempt at a Solution I have tried using the two formulas above but i couldn't show the required result.

I tried to solve it but confused. Pls. help me to solve this equation: dy/dx + (e^x)*Sec(y) = Tan(x); (hint: integrating factor is e^-ax, and a is unknown, a ε ℝ, find it, solve the equation) Thnx.