Trigonometric Definition and 1000 Threads

1. Prove:\frac{cscx +cotx}{cscx-cotx} = \frac{1+2cosx+cos^2x}{sin^2x} Homework Equations tanx = \frac{sinx}{cosx} cotx = \frac{cosx}{sinx} cscx secx cotx sin^2x + cos^2x = 1 The Attempt at a Solution Left side: =\frac{cscx +cotx}{cscx-cotx} =\frac{1/sinx + cosx / sinx}{1/sinx - cosx/sinx}...

So I'm trying to get through euler's introduction to the analysis of the infinite so I could eventually read his books on calculus but I'm stuck somewhere and can't seem to figure out how he equates this identity so by expanding I get sin(2y) * cos(z) + cos(2y) * sin(z). I get that the...

Here is the question: Here is a link to the question: Help with trig equation :)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: Express in the form a + bi, where a and b are real numbers.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

"Sum to Product" Trigonometric identity does not work Hi, The identity sin(u) + sin(v) = 2 * sin (\frac{u+v}{2}) * cos(\frac{u-v}{2}) http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities Does not always work. I put the equation : (sin(u)...

Evaluate \cos \left(\frac{\pi}{65}\right)\cdot\cos \left(\frac{2\pi}{65}\right)\cdot\cos \left(\frac{4\pi}{65}\right)\cdot\cos \left(\frac{8\pi}{65}\right)\cdot\cos \left(\frac{16\pi}{65}\right)\cdot\cos \left(\frac{32\pi}{65}\right).

Here is the question: Here is a link to the question: Prove the identity, pre calc!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Decompose the expression below into real factors: 1-\sin^5 x-\cos^5 x

i got sinx/siny=1.2 and i need to find cosx/cosy can i do it or maybe i need more knowledge?

Homework Statement Given (e^(ix) - 1)^2 , show that it is equal to 2-2cosx Homework Equations e^ix = cosx + isinx The Attempt at a Solution After subbing in Euler identity and expanding I get: cos(x)^2+sin(x)^2-2cosx-2jsinx+2jcosxsinx + 1 after using the addtion formulas I get...

Find the minimum value of |\sin x+\cos x+\tan x+\cot x+\sec x+\csc x| for all real numbers x.

Homework Statement Can you all help? The problem is 2 sin(x/2) - 1 = 0 I don't know what to do with the (x/2). The Attempt at a Solution So far I've done this: 2 sin(x/2)-1=0 2 sin(x/2)=1 sin(x/2)=1/2

1. The problem statement Find the sum of the series: a. 1 + a cos θ + a^{2} cos 2θ + a^{3} cos 3θ + ... + a^{n} cos nθ Apparently, the answer is: \frac{a^{n+1}(a cos nθ - cos(n+1)θ) - a cos θ + 1)}{a^{2} - 2a cos θ + 1} 2. The attempt at a solution = The real part of z^{0} +...

Homework Statement Given the following two triangles: Show that v \cos{\delta} = V(1-\cos{\beta})+u\cos(\alpha - \beta) The Attempt at a Solution Using the cosine law I've got: v^{2}=x^{2}+V^{2}-2xV\cos{(\theta + \beta)} and u^{2}=x^{2}+V^{2}-2xV\cos{(\theta)} I figured maybe using the...

Homework Statement Let R = \{ (x,y) \in \mathbb{R^{2}}: 0<x<1, 0<y<1\} be the unit square on the xy-plane. Use the change of variables x = \frac{{\sin u}}{{\cos v}} and y = \frac{{\sin v}}{{\cos u}} to evaluate the integral \iint_R {\frac{1} {{1 - {{(xy)}^2}}}dxdy} Homework Equations...

Find x such that trigonometric \dfrac{\sin (3x) \cos (60^{\circ}-x)+1}{\sin (60^{\circ}-7x)-\cos (30^{\circ}+x)+m}=0 where m is a fixed real number. Hi all, I know the expression in the numerator has no real roots by checking it at W|A (plot the graph of y=sin(3x)cos(pi/3 -x)+1 -...

Homework Statement When integrating a function of the form: \displaystyle\int_c^d { (sinx)^{a} * (cosx)^{b}} Is this a correct simplification of the rules to evaluate: 1. if exponent on sin or cos is odd, and the other is even, separate out one of the odd's and use an identity on the...

Homework Statement (question attached) Homework Equations The Attempt at a Solution Checking solution.. pretty sure I did this wrong. (solution attached)

Homework Statement Simplify the following trigonometric expression: cscθtanθsecθ Homework Equations tanθ = sinθ/cosθ sin^2θ + cos^2θ = 1 cscθ = 1/sinθ secθ = 1/cosθ cotθ = 1/tanθ The Attempt at a Solution I just want to double check my solution. cscθtanθsecθ = 1/sinθ x...

I have shown the first part that they ask for. For the second part: let tanθ = t tan(3\theta) = \displaystyle\dfrac{tan(2\theta) + tan\theta}{1-tan(\theta)tan(2\theta)} = \dfrac{\frac{2t}{1-t^2} + t}{1 - t(\frac{2t}{1-t^2})} hence t = 2 + \dfrac{3t - t^3}{1-3t^2} t^3 - 3t^2 + t + 1...

Homework Statement Sin(tan(2x)) With respect to x Homework Equations Differentiation The Attempt at a Solution My question is whether I can simply use d/dx (Tan x) = Sec^2(X) to extrapolate that to d/dx(tan 2x) = Sec^2(2x) ? Or do I have to convert to sine/cosine and go from...

Homework Statement ∫cot^2(x)csc^4(x)dx Homework Equations The Attempt at a Solution ∫cot^2(x)(cot^2(x)+1)csc^2(x)dx u=cot(x) du=-csc^2(x)dx -∫u^2 (u^2 +1)du -∫u^4 + 2u^3 + u^2 du -(u^5)/5 - (u^4)/2 - (u^3)/3 -cot^5(x)/5 - cot^4(x)/2 - cot^3(x)/3 + C Wolfram alpha shows the solution as...

Hello, I got problem with A homework "find an equation of the tangent line to curve at the given point. $y=sec(x)$. $(pi/3,2)$ progress: $y'=sec(x)tan(x)$. So basicly that sec(x) don't say me much so i rewrite it as $1/cos(x)$ $y'=1/cos(x)•tan(x)$ now i can put $pi/3$ on the function to...

Homework Statement g(x) = 4∏ [cos(3∏x) sin (3∏x)]The Attempt at a Solution g(x) = 4∏ [cos(3∏x) sin (3∏x)]' 4∏{[cos (3∏x)][sin(3∏x)]' + [sin(3∏x)][cos(3∏x)]'} = 4∏{[cos (3∏x)][cos(3∏x) . (3∏)] + [sin(3∏x)][-sin(3∏x) . (3∏)] = Now, my question is: Can I combine the numbers and have the...

Hello, Im currently on chapter about derivate trigonometric functions. It have been hard for me to understand this sec,cot,-csc? Why do you rewrite example $1/cos^2x$ as $sec^2x$? when I get like sec,csc etc i kinda feel i have no clue what it means. Then you think what do Petrus mean? example I...

Find y^{I} (sinxsecx)/1+xtanx The supplied answer is 1/(1+xtanx)^{2} I got stuck with an extra x on top at the end. Where did I mess up at? y^{I}(sinxsecx)/1+xtanx = [1+xtanx*f^{I}(sinxsecx)-sinxsecx*f^{I}(1+xtanx)]/(1+xtanx)^{2} =...

Homework Statement evaluate the integral. Homework Equations integral (pi/6 to pi/4) [(sin2x)^4 / sqrt(1-cos2x) dx] The Attempt at a Solution 1. multiplying by conjugate: sqrt(1+cos2x)/sqrt(1+cos2x) . 2. should i split the (sin2x)^4 into (1-(cos2x)^2)^2 ?

Homework Statement solve the integral.Homework Equations integral (5pi/6 to pi) (cosx)^4 / sqrt(1-sinx) dxThe Attempt at a Solution Following the solution manual: integral (5pi/6 to pi) ( (cosx)^4 / sqrt(1-sinx)) * sqrt(1+sinx)/sqrt(1+sinx) however i am not sure how to do the algebra here...

Homework Statement integral (1)/(x^2sqrt(36-x^2) Homework Equations The Attempt at a Solution I found X=6sinθ dx=6cos √(36-x^2)=√(36-sin^2θ)=6cosθ i think the problem is that i am not getting integral of ∫csc^2θ

Here is the question: Here is a link to the question: Given 0<x<orequalto 1, determine the value of inversine (x) + inversetan (squareroot(1-x^2)/x)? - Yahoo! Answers I have posted a link there to this topic so the OP may find my response.

I am unsure whether I have properly performed the integration of the integral ∫((sin(√x))^3*dx)/√x When I used my TI-Nsprire CAS to take the derivative of my answer in order to check if I was correct, and it came out differently. Now I used some trig identities to manipulate the problem, so I...

Homework Statement evaluate the definite integral ∫(0 to 3) dx/sqrt(25+x^2) Homework Equations The Attempt at a Solution I first used substitution and set x=5tanθ, and dx=5tanθsecθdθ then i wrote the integral as 5∫ tanθsecθdθ/sqrt(25(1+tan^2(θ)) after some simplification i...

Homework Statement Use Equation (1) to derive the formula: (1-a*cos(phi))/(1-2*a*cos(phi)+a^2))= 1+a*cos(phi)+a^2(cos(2phi))+a^3(cos(3phi))... Homework Equations Equation (1) is 1/(1-a(cos(phi)+isin(phi)))= 1+ [a(cos(phi)+isin(phi)]+ [a(cos(phi)+isin(phi)]^2 +...

Here is the question: Here is a link to the question: http://answers.yahoo.com/question/index?qid=20130130130636AAOqgvz I have posted a link there so the OP can find my response.

Here is Katie's question: Here is a link to the original question: Solve for x in the equation 1+sinx/cosx + cosx/1+sinx = 4 for 0 < x < 2pi? - Yahoo! Answers I'll post a link there to this topic so the OP can find my response.

Please consider the following equation: $\displaystyle \sum_{k=1}^{n}\cos^4\left(\frac{k\pi}{2n+1} \right)=\frac{6n-5}{16}$ For this particular equation, which I am trying to prove is true, I have found no way to crack it, even if I let $n=2$ and begin to try to combine the terms together...

If we see the form \sqrt { { a }^{ 2 }-{ x }^{ 2 } }, we always set x=asinθ How do we know that it will work in advance? Just trial & error?

I want to prove this equation: \cos\left(\frac{2\pi}{5}\right)+\cos\left( \frac{4\pi}{5}\right)+\cos\left( \frac{6\pi}{5}\right)+\cos\left(\frac{8\pi}{5} \right) = -1 . I've no idea how to begin. I think it may be related to complex numerd but I don't know how to combine them.

Homework Statement Show, using complex numbers, that sin(x)+cos(x)=(√2)cos(x-∏/4) Homework Equations cos(x)=(e^(ix)+e^(-ix))/2 sin(x)=(e^(ix)-e^(-ix))/2i e^ix=cos(x)+isin(x) The Attempt at a Solution I was given the hint that sin(x)=Re(-ie^(ix)), but have thus far not been...

Homework Statement Solve cot^{-1} x - cot^{-1} (n^2 - x+1)=cot^-1(n-1) Homework Equations The Attempt at a Solution I can write the above equation as θ+α=β where the symbols represent the respective inverse functions. Now I take tan of both sides. Simplifying I get...

My task is to solve the integral \frac{1}{\cos 2z} on the contour z=|1| using a Laurent series. The easy part of this is the geometric part. I drew a picture of the problem. I see that there are two singularity points that occur within the contour region at \pm \frac{\pi}{4}. I realize...

Hello, when I have to solve a trigonometric problem I can easily figure in my mind sin and cos, but how can I figure tan ?

Studying for finals here...So I have this specific problem to use trig substitution on. $$\int \frac{x^2}{\sqrt{1-x^2}}\,dx$$ I begin by substituting $$x={sin{\theta}}$$ I am fine with doing everything up to the point where I have an answer for the integral in terms of \(\theta\). This...

I have always capitalised the first letter of my trigonometric functions, for example, writing Sinθ as opposed to the usual sinθ. Is it wrong to capitalise them? Does it make a difference in meaning?

Homework Statement Express the function f(x) = -2sin(3x) -4cos(3x) in the form of a general sine finction. Identify the amplitude, period, and phase shift Homework Equations sinx/cosx = tanx sin2x + cos2x = 1 The Attempt at a Solution don't know how to start don't...

Homework Statement Solve each equation for solutions on the interval 0 ≤ x ≤ 2∏. 2 sin x = √3 The Attempt at a Solution Okay so I was able to solve this one: 2 sin x = √3 sin x = (√3) / 2 So i got x = ∏/3 ; 2∏/3 ; 4∏/3 ; 5∏/3 I substituted the x's into the original...

Homework Statement Find the exact value of the given expressions. sin (2 sin-1 (4/5)) or sin (2 arcsin (4/5)) Just two different ways of writing it Homework Equations maybe The Attempt at a Solution I've only gotten this far: sin (2 arcsin (4/5)) = 2 sin (arcsin (4/5))...

Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression Z= (Z_1 Z_2)/(Z_1+ Z_2 ) If Z1 = 4 + j10 and Z2 = 12 – j3, calculate the impedance Z in both rectangular and polar forms. Homework Equations j2=-1 The Attempt at a Solution Z=...

Homework Statement Show that: ∫f(sin(x))dx = ∫f(cos(x))dx where each integral is over the limits [0, \pi/2], for a 'well behaved' function f. 2. The attempt at a solution I have tried relating sin(x) and cos(x) and somehow rearrange one of the integrals to look like the other. Since...

Homework Statement tg(4x) = 1 The Attempt at a Solution I have a doubt about the part I have to add to the result, are these solutions correct ? 4x = 45° + n * pi x = 11,25° + n * (pi/4) Thanks