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.
Homework Statement
\int_{1}^{5}\sqrt{4-(x-3)^2}dx
Homework Equations
The Attempt at a Solution
Not really a homework. Just curious.
Let x-3=2sin u
x=2sin u+3
Now limit change,
when x=1, u = arcsin (-1)
when x=5, u = arcsin (1)
Since there are infinitely many solution...
Hello all,
I was wondering if someone has ever found a purely algebraic proof for the addition/subtraction theorems of trigonometry, mainly sin(a+b)=sin(a)cos(b)+sin(b)cos(a). Given a right triangle:
Let x be one of the perpendicular legs and let the other leg be composed of two parts, y1...
Hi! I'm just a beginner i don't know much about trigonometry... can you tell me how to convert the trigonometric ratios to degree.. for example:
o.3333 how did it become 19.47degree ? i saw it in the book... can you tell me how? I know this is simple for you all! i want to solve it without using...
Homework Statement
Here is the question given:
A blade for a lawnmower consists of two parts made of the same material and joined together as shown:
The length OP is one unit in length and MPQN is square in shape.
Develop an equation for the cross-sectional area of the blade and...
Homework Statement
Prove that:
tan^2∅/tan∅ - 1 + cot^2∅/cot∅ - 1 = 1 + sec∅cosec∅
Homework Equations
The Attempt at a Solution
I have solved the question taking tan∅ = sin∅/cos∅.
But I want to solve it some other way.
Homework Statement
lim of (sin(x)/(x+sin(x)) as x approaches 0
Homework Equations
none
The Attempt at a Solution
I tried using trigonometric identites to figure it out but I can't do it, and when I looked up help for it I only found solutions that utilize the l'hopitals rule. I...
Homework Statement
Hello! I'm having some trouble to find this limit \lim_{x\rightarrow \pi}\frac{senx}{x-\pi } Also, limits like this one \lim_{x\rightarrow \frac{\pi}2{}}\frac{1-senx}{2x-\pi } confuse me a lot!Homework Equations
The Attempt at a Solution
I don't even know where to start! I...
it's bothering my brain..i thought about it many times...i can't make intuition of it
can anyone prove it?
oh by the way... C = Sqrt[A^2 + B^2] and theta is equal to arctan(B/A)
hey,
(1-{{x}^{2}}){{y}^{''}}-2x{{y}^{'}}+n(n+1)y=0,\,\,\,\,\,-1\le x\le 1
to convert the legendre equation y(x) into trig form y(cos\theta) is it simply, set x=cos\theta then
(1-{{\cos }^{2}}\theta ){{y}^{''}}-2{{y}^{'}}\cos \theta +n(n+1)y=0 for -\pi \le x\le \pi
{{\sin }^{2}}\theta...
Homework Statement
I'm trying to solve two similar equations, but I can't go on.
This is the first one
http://img818.imageshack.us/img818/298/imageevsu.jpg
This is the second one:
http://img7.imageshack.us/img7/7812/imageowud.jpg
Homework Equations
The Attempt at a Solution...
Homework Statement
cos(x-y)cosy-sin(x-y)siny=cosx
a.try to prove that the equation is an identity
b. determine a counterexample to show that it is not an identity
Homework Equations
cos(x-y) = cosxcosy+sinxsiny
sin(x-y) = sinxcosy-cosxsiny
The Attempt at a Solution
a.Left side of...
Homework Statement
Solve the differential equation: \frac{dy}{dx} = cos^2 (x) cos^2 (2y)
The Attempt at a Solution
I rewrote the equation
\frac{dy}{cos^2 (2y)} = sec^2 (2y) = cos^2 (x) dx. Then I integrated,
\frac{tan(2y)}{2} = \frac{1}{2} (x + sin(x)cos(x)) + c. Then I solved for y...
Homework Statement
http://img35.imageshack.us/img35/806/imagezxg.jpg Homework Equations
The Attempt at a Solution
http://img853.imageshack.us/img853/4035/imageyffi.jpg
The problem is to solve the integral of :
dx / (x^2(9-4x^2)^(1/2)) using trig substituition, which I really don't understand.
Formula's that are useful:
The integral table
Integral 1/(u^2(a^2-u^2)^(1/2))=
-((a^2-u^2)^(1/2)) / (ua^2)
Work so far:
Figuratively banging my head...
Homework Statement
consider the function
f(n,x) = (sinx+sin2x+sin3x +...+sin(n-1)x+sinnx)/)cosx+cos2x+cos3x+...+cos(n-1)x+cosnx)
Find the sum of all values for which f(23,x) = f(33,x)where x is measured in degrees from 100<x<200
Homework Equations
you get obviously tanx+tan2x...
Homework Statement
find the value(s): cot(2sin^(-1) 2/7)
The Attempt at a Solution
I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came...
Homework Statement
Not long ago I had a similar problem, which I was able to solve after reading this thread, but for this question I'm stuck and I could use a small hint.
Homework Equations
The Attempt at a Solution
Thanks
1. Sin^2(x) = 3 – x
Answer: 2.97
Attempts:
1-cos^2(x) = 3 – x
cos^2(x) - x + 2 = 0
Factored it and got x = pi = 3.14
It’s a multiple choice question, and other answers were 3.02,3.09 which are few decimal places off so the answer must not be pi since it's not even a choice. Is the...
Homework Statement
Find the derivative of:
sqrt(x^2-4)-2tan^-1{.5*sqrt(x^2-4)}
Homework Equations
U'/1+U^2
U'=x/2sqrt(x^2-4)
1+U^2=x^2
The Attempt at a Solution
I combined the above components but my answer is incorrect. I feel that I might have the wrong answer for...
Hi everyone,
Homework Statement
My problem is just to derive a simple formula, which is
http://www.texify.com/img/%5Cnormalsize%5C%21%28-1%29%5E%7Br%28r%2B1%29/2%7D%20%3D%5Csqrt%7B2%7D%20%5Cmbox%7Bcos%7D%20%5Cfrac%7B%5Cpi%7D%7B4%7D%282r%2B1%29.gif
Here r is a positive integer.
The Attempt...
Homework Statement
Find the derivative of f(x) = 1/4 sin^2 2x
Homework Equations
The Attempt at a Solution
f'(x) =1/4(sin 2x)^2
f'(x) = 1/4*2(sin 2x)(cos 2x)
f'(x) = 1/4(sin 4x)
That is my answer to the problem, but the book has it as f'(x) = 1/2(sin 4x)
What did I do...
Hello math helpers and others. Before I ask my question I would like to say that I appreciate everyone's help on these boards, and I hope that I will not be too large of a nuisance in the future. I am in my first calculus class, and it appears that I am going to need a lot of help. I was a...
Hello,
do you have any strategy to suggest in order to solve the following system of partial differential equations in x(s,t) and y(s,t)?
\frac{\partial x}{\partial t} = x - \frac{1}{2}\sin(2x)
\frac{\partial y}{\partial t} = y \; \sin^2(x)
(note that the partial differentiation is always with...
Homework Statement
solve the following limit: \lim_{x\rightarrow0}\frac{x+sinx}{2x-sin3x}The Attempt at a Solution
I know the principle of solving all sorts of limits but not trig limits, and since we just started trig limits it's still not clear to me, but i think to solve it we have to...
Homework Statement
tan(\alpha)=\sqrt{2}-1 for every alpha in ]0,90°[
Homework Equations
1-count tan(2α)
2-conclude the value of α
The Attempt at a Solution
1-after using tan(2α)=(2tanα)/1-tan^2α) i got tan(2α)=(√2-1)/2
2- I know that α is pi/8 but i just don't know how to...
Homework Statement
I don't understand why the x/2 is not being integrated. I would think one should use u substitution. u = x/2, du = x, but they're not doing that.
I was messing around proving the area of a circle using trigonometric substitution. However, I ended up with area = -πr^2.
In my integral I ended up using trigonometric substitution and setting x = r*cos(theta)
However, this yields x = -r*sin(theta)*d(theta).
When that's substituted...
Homework Statement
I don't see how they're going from
sec x cot x to csc x
and
csc x tan x to sec x
The derivative of sec x is sec x tan x not csc x tan x
and the derivative of csc x is -csc x cot x
and if it's an identity then they didn't care to inform me of that at...
Homework Statement
The question asks me to evaluate the indefinite integral:
sin2x/(1+(cos2x)^2)
The (cos2x)^2 is read cos squared 2x, i just don't know how to put the squared before the 2x and not have it look confusing !
Homework Equations
The Attempt at a Solution
To be...
Homework Statement
I understand everything except why the derivative of 2 + tan (x/2) is .5 + sec^2(x/2)
I don't understand the .5 part. I understand the sec part. I would think the derivative of 2 would be C, or just disappear.
Prove that:
\[ \int_{0}^{\pi/2} \cos(nx) \cos^n(x) dx =\frac{\pi}{2^{n+1}}\]
\[ \int_{0}^{\pi} \frac{1-\cos(nx)}{1-\cos(x)} dx =n\pi \]
where \( n \in \mathbb{N} \). You can use induction, contour integration or any other method you like.
Homework Statement
Prove that (for every x smaller than -1)
\displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}}+arccotx=\pi
Homework Equations
The Attempt at a Solution
So i split the formula into two parts:
\displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}} and \displaystyle...
I found this question on a website.
Homework Statement
Prove that \displaystyle \int_{0}^{\pi}\frac{1-\cos(nx)}{1-\cos(x)} dx=n\pi \ \ , n \in \mathbb{N}
2. The attempt at a solution
Here's my attempt using induction:
Let P(n) be the statement given by...
Homework Statement
arctan(8x-8)=-1
Homework Equations
I'm sure what this part wants.
The Attempt at a Solution
tan[arctan(8x-8)]=tan(-1)
8x-8=tan(-1)
x=(1/8)(tan(-1)+8)
x=(1/8)(-(tan(1)+8)
x=
I am stuck on the last part since the homework says Simplify the above equation...
Homework Statement
prove that for any integer n
tannθ = ((n choose 1)tanθ - (n choose 3)tan^3θ + (n choose 5)tan^5θ)-.../ (( n choose 0) -(n choose 2)tan^2θ + (n choose 4)tan^4θ-...)
The first 3 numbers on top and bottom look like these however the sum and differences keep going, and you...
Homework Statement
basically i have this proof to do where (cot5x * [trigonometric function]5x)/csc6x = 5/6 and i have to prove it equals 5/6
Homework Equations
but what i can't remember about the problem is the second function. I've tried plugging in all of them and using a made up value of...