Trigonometric Definition and 1000 Threads

Is it possible to express (cos(\theta)sin(\theta))^2 in terms of spherical harmonics?

Homework Statement $$f(x)=sin2x+cos4x$$ Homework Equations The Attempt at a Solution $$The\quad period\quad of\quad sin2x\quad is\quad π.\quad The\quad period\quad of\quad cos4x\quad is\quad \frac { π }{ 2 } .\\ \\ What\quad is\quad the\quad period\quad of\quad f(x)?$$

Homework Statement Evaluate sin^-1(cos70°) Homework Equations The Attempt at a Solution sin^-1(cos70°)=θ sinθ=cos70° sinθ=1/2 sinθ=∏/3

Here is the question: I have posted a link there to this topic so the OP can see my work,

any hints on how to work out this problems. $\displaystyle\int\frac{dx}{(1-sinx)^2}$ $\displaystyle\int\sin x\sin2x\sin3x dx$ thanks!

i was thinking hard how to integrate this, but none of the techniques I know did work. please kindly help with this matter. thanks! $\displaystyle\int\sqrt{1+\cos\theta}d\theta$

i'm kind of unsure of my solution here please check. $\displaystyle\int \sin^3x\cos^3x= \int(\sin x \cos x)^3 =\int(\frac{1}{2}\sin2x)^3=\frac{1}{8}\int \sin^3 2x dx$ $\displaystyle u=2x$; $\displaystyle du=2dx$; $\displaystyle dx=\frac{1}{2}du$ $\displaystyle \frac{1}{8}\int...

Homework Statement d/dx(sec(x)/1+tan(x) Evaluate at x=∏/6 Homework Equations The Attempt at a Solution ((1/cos(x))(1+tan(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))^2 ((1/cos(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x)) I used the quotient rule and reduced what I could. Have I done this...

Prove that: $\displaystyle\sum_{k=0}^n \frac{\cos(k x)}{\cos^kx} = \frac{1+(-1)^n}{2\cos^nx} + \dfrac{2\sin\big(\lfloor\frac{n+1}{2}\rfloor x\big) \cos\big(\lfloor\frac{n+2}{2}\rfloor x\big)} {\sin x\cos^n x} \qquad\qquad (\frac{2x}{\pi}\not\in \mathbb Z)$ *note: $\lfloor x\rfloor$ is floor...

Homework Statement 2 sin(2x) = 2 cos(x) Homework Equations The Attempt at a Solution 4sinxcosx-2cosx=0 2(2sinxcosx-cosx)=0 2cosx(sinx-1)=0 2cosx=0 sinx=1 And then I did the math and got pi/2 and 3pi/2 , but that's apparently wrong.

Can anyone please help to solve this following integral? ∫(sin(x)-sin^2 (x)/√(sin^2 (x)+c)) dx c is a constant

What tells me that when I need to integrate it I can't just do (25-x^2)^0.5 and go on from there with common power of x integration? What is the thing that tells me "hang on there, this requires trigonometric integration"?

1. ∫\frac{\sqrt{x^{2}-4}}{x} dx, x=2secθ, dx=2secθtanθ dθ 2. \sqrt{x^{2}-a^{2}},sec^{2}θ-1=tan^{2}θ 3...

Prove that $$\tan 20^{\circ}+4 \sin 20^{\circ}=\sqrt{3}$$.

Homework Statement Solve for y': 4[(cos x)(cos y)(y') + (sin y)(-sin x)] = 0 Homework Equations none The Attempt at a Solution 4[(cos x)(cos y)(y') + (sin y)(-sin x)] = 0 4y' (cos x) (cos y) - 4 (sin x) (sin y) = 0 4y' (cos x) (cos y) = 4 (sin x) (sin y) y' = [4 (sin...

find the values of other five trig functions $\csc\theta=-2\,and\, \cot\theta>0$ my solution $x=-2$ $y=-1$ $r=\sqrt{5}$ $\displaystyle \sin\theta=-\frac{1}{\sqrt{5}}$ $\displaystyle\cos\theta=-\frac{2}{\sqrt{5}}$ $\displaystyle\cot\theta=2$ $\displaystyle\tan\theta=\frac{1}{2}$...

can you explain to me what my trigonometry book say "the value of each ratio is determined only by the angle $\theta$ and not by the particular point $P(x,y)$ on the terminal side; that is , the value of the ratio is a function of the angle $\theta$." what does "determined only by angle...

How to prove: Cosθ < (Sinθ)/θ < 1/Cosθ when 0<x<1/2π : π is Pie It seems to be a fundamental inequality that Apostol calculus uses in its text. Thank you

Evaluate $$\tan\frac{\pi}{13}\tan\frac{2\pi}{13}\tan\frac{3 \pi}{13}\tan\frac{4\pi}{13}\tan\frac{5\pi}{13} \tan \frac{6\pi}{13}$$.

I will do my best to describe the problem I am working on. The problem is not from a textbook or anything but something I am working on independently to strengthen my first year calculus knowledge. What I did is I took sin(x) and -sin(x) and graphed them together. Sin(x) and -sin(x)...

Solve $$2\sin^4 (x)(\sin((2x)-3)-2\sin^2 (x)(\sin((2x)-3)-1=0$$.

Homework Statement Solve: 2 tan x (tan x - 1) = 3. Homework Equations Pythagorean identities? The Attempt at a Solution I tried the following: 2 tan^2 x - 2 tan x = 3 2 (sec^2 x - 1) - 2 tan x = 3 2 (1 - cos^2 x) - 2 sin x cos x = 3 cos^2 x (multiplying through by cos^2 x)...

Homework Statement Given that -180 <= x <= 180, solve the following equation in radians cosx = -1/sqrt(2) The Attempt at a Solution I'm not exactly sure how to solve this question with respect to the range -180 <= x <= 180. I know that -1/sqrt(2) means that x is 45 degrees in either...

Solve the equation $$\sqrt{3}\sin x(\cos x-\sin x)+(2-\sqrt{6})\cos x+2\sin x+\sqrt{3}-2\sqrt{2}=0$$

Homework Statement If ##\displaystyle \tan\left(\frac{\pi}{4}+\frac{y}{2}\right)=\tan^3\left( \frac{\pi}{4}+\frac {x}{2} \right)##, prove that $$\frac{\sin y}{\sin x}=\frac{3+\sin^2 x}{1+3\sin^2x}$$Homework Equations The Attempt at a Solution...

Homework Statement Find the exact value, without using a calculator. \ cos(\frac{\pi}{15}) \ cos(\frac{\pi}{45}) The Attempt at a Solution I started off using a product to sum formula- \frac{1}{2}[cos(\frac{4\pi}{45})+ \ cos(\frac{2\pi}{45})] Now I don't know where to...

Homework Statement If ##A+B+C=\pi##, prove that ##\cos A+\cos B+\cos C \leq 3/2##. Homework Equations The Attempt at a Solution I don't really know how to start. ##A+B=\pi-C##. Taking cos on both sides doesn't seem of much help. I need a few hints to start with.

Hello. I was doing a (simple) physics problem and stumbled with a mathematical problem. I was doing a projectile motions problem and I have set up my equation like this:Δx = Vi (cosθ) (t) 270= 25cosθ t t = 270 / (250cosθ) And this is where I'm having problems. I know from my high school trig...

Homework Statement \cos x-\sqrt{3}\sin x=\cos(3x) Homework Equations The Attempt at a Solution Dividing both the sides by two i.e \cos x \cos \frac{\pi}{3}-\sin x \sin \frac{\pi}{3}=\cos (3x)/2 LHS can be written as ##\cos(x+\pi/3)##. Substituting ##x+\pi/3=t \Rightarrow...

Please tell me if i worked out the problem correctly. 1. ∫(dx/x2-x+2) completing the square of the denominator i have, ∫[dx/(x-1)2+12] a=1, u=x-1; du=dx ∫(du/a2+u2) 1/1*tan-1x-1/1 + c = tan-1x-1 + C -->> final answer 2. ∫[dx/(15+2x-x2)1/2] ∫[dx/(14-(x-1)2)1/2] ∫{dx/([(14)1/2]2-(x-1)2)}...

Hello I am trying to solve the integral of the next function: 1/(1+cos(x)) and without using the substitution rule...any ideas ? thanks !

Without the use of a calculator, evaluate $$\tan^2 20^{\circ}+\tan^2 40^{\circ}+\tan^2 80^{\circ}$$.

Homework Statement I want to derive the trig identities starting with rotation on the plane. Homework Equations One rotation through a given angle is given by $$x' = xcosθ - ysinθ $$ $$y' = xsinθ + ycosθ$$ The Attempt at a Solution What if I wanted to rotated through any...

Show that : \left( {\sin x + a\cos x} \right)\left( {\sin x + b\cos x} \right) \leq 1 + \left( \frac{a + b}{2} \right)^2

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

Hi, I am just wondering what the antiderivative of this integral was. It looks easy to me, but I no matter what I did just could not evaluate it. Can someone help me?: $$\int \frac{\tan(x)}{x}\;dx$$

Solve $$\sqrt{2}\cos \left(\frac{x}{5}-\frac{\pi}{12} \right)-\sqrt{6}\sin \left(\frac{x}{5}-\frac{\pi}{12} \right)=2\left(\sin \left(\frac{x}{5}-\frac{2\pi}{3} \right)-\sin \left(\frac{3x}{5}+\frac{\pi}{6} \right) \right)$$

Okay, so I know how to apply basic trigonometric functions to solve right triangles. However, I am not quite sure how to manipulate trigonometric functions to solve for more complex questions involving non-right triangles, like the question I have attached. I have to use the basic trigonometric...

Homework Statement Integral (11x^2)/(25-x^2)^(3/2) dx from 0 to (5*sqrt(3))/2 Homework Equations sin^2(θ) = 1 - cos^2(θ) The Attempt at a Solution 1. Factor out 11 from integral for simplicity. 11 * integral (x^2)/(25-x^2)^(3/2) 2. Re-write denominator of integral to...

Prove $$\frac{\sin\left(5\tfrac{3}{4}^{\circ} \right)}{\cos\left(17\tfrac{1}{4}^{\circ} \right)}+\frac{\sin\left(17\tfrac{1}{4}^{\circ} \right)}{\cos\left(51\tfrac{3}{4}^{\circ} \right)}+\frac{\sin\left(51\tfrac{3}{4}^{\circ} \right)}{\cos\left(155\tfrac{1}{4}^{\circ}...

Solve the equation $$\cos^2 \left(\frac{\pi}{4}(\sin x+\sqrt{2}\cos^2 x)\right)-\tan^2 \left(x+\frac{\pi}{4}\tan^2 x\right)=1$$

Homework Statement cos 2x + cos 4x = cos x 0 degrees ≤ X ≤ 360 degrees Homework Equations Trig identities. The Attempt at a Solution Trig identities and equations are my weakness so I'm trying to review some to get better at them, so I guess this isn't technically homework...

Here is the question: Here is a link to the question: PRE-CALC QUESTION!? HELP !? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Trigonometric functions -->sine function EASY! Homework Statement Consider the trigonometric function f(t)=-1+4sin(0.5π(t-1)). (a) What is the amplitude of f(t)? (b) What is the period of f(t)? (c) What are the maximum and minimum values attained by f(t)? Homework Equations...

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 [SIZE="3"]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...

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