Help with a Trigonometric identity...
Homework Statement
(sin x + sin 2x + sin 4x) / (cos x + cos 2x + cos 4x) = tan 2x
Homework Equations
sin 2x = 2sinxcosx; cos 2x = cos^2x - sin^2x
The Attempt at a Solution
solving left side,
=[sin x + sin 2x + sin (2x + 2x)]/[cos x + cos...
Homework Statement
\int\frac{secx}{(tanx)^2}dx
The Attempt at a Solution
I tried all the u subs u=tanx and u=secx
but neither worked.
Should I used other methods?
Please help me with the start!
Homework Statement
(1-cos^2x)(1+tan^2x) = tan^2xHomework Equations
N/AThe Attempt at a Solution
(1-cos^2x)(1+tan^2x) = tan^2x
L.S.
= (sin^2x)(1+sin^2x/cos^2x)
= sin^2x+(sin^4x/cos^2x)
Now, I get a common denominator, but it's not doing anything for me. Did I do the right thing in converting...
Homework Statement
sinx + cosx = 0Homework Equations
N/AThe Attempt at a Solution
sinx + cosx = 0
sinx = -cosx
sinx = (+/-) sqrt(sin^2x - 1)
(sinx)^2 = (+/-) sqrt(sin^2x - 1)^2
sinx = sin^2x - 1
Not really too sure what to do from here on.
The answer is 3\pi/4 and 7\pi/4.
I appreciate the...
Homework Statement
Determine the points of intersection for the two given functions on the interval 0<x<4pi
y = 2 \sin \frac{x}{2}
y = 3 \cos \frac{x}{3}
2. The attempt at a solution
Well i tried graphing it and found out that the solution must lie somewhere between pi and 2pi...
1.A kite 40 m above the ground moves horizontally at the rate of 3 m/s. At what rate is the angle between the string and the horizontal decreasing when 80 m of string has been let out. Answer is 0.02 m/s
2. What I did was:
-Drew a triangle as prescribed above
-I found the unknown...
Homework Statement
Maybe I'm just blind, but how is
T_n(x)=\left(\frac{1+\cos(t-a)}{b}\right)^n
of the form
T_n(x)=\sum_{k=-n}^nc_ke^{ikx}
?
I can get
\left(\frac{\cos(t-a)}{b}\right)^n
by setting
c_{\pm n}=\left(\frac{e^{\mp ia}}{2b}\right)^n
and the rest of the c_k= 0, but how does...
I need some help on 15 identities problems to help me study for my math final.
They are blurry and somewhat hard to read, but if anyone wants to take a crack at some of them they are here:
http://img407.imageshack.us/img407/5696/math1lh2.jpg...
Hi,
as I was studying complex numbers today I came across this, and I couldn't explain it:
1=e^{i0}
1=e^{i2\Pi}
1^{1/2}=e^{i2\Pi/2}
1=e^{i\Pi}
1=-1
Where is the mistake?
Thank you very much for your help.
I remember learning an iterative method that gives the answer to trigonometric polynomials such as
sin(x)-0.7-0.611cosx = 0
where x is the angle in degrees.
The person who I learned this method from called it the method for solving transcendentals. Now I can't seem to find any...
Homework Statement
Find the range of the function: y=(2cosx+1)/(2cosx-1) algebraically
Homework Equations
Reducing it, I obtained: y= tan(3x/2)/tan(x/2), but the discontinuity confuses me
The Attempt at a Solution
I did it with my calculator and this is the result:
Ran =...
[SOLVED] Series with Trigonometric funtions
Homework Statement
Determine whether the series converges conditionally,converges absolutely or diverges.
\sum_{n=2}^{\infty}\frac{\sin (n+\frac{1}{n})}{\ln (\ln n)}
The Attempt at a Solution
\frac{\sin (n+\frac{1}{n})}{\ln (\ln...
Homework Statement
Determine whether the series converges and diverges.
\sum_{n=3}^{\infty}\ln \left(\frac{\cosh \frac{\pi}{n}}{\cos \frac{\pi}{n}}\right)
The Attempt at a Solution
\sum_{n=3}^{\infty}\ln...
This isn't really a homework question--but just something I was thinking about while doing homework.
Since lim(sinx/x) as x--->0 = 1
does that mean that lim(x/sinx) as x--->0 = 1 ?
I'm not sure about answer.It looks very strange.
Homework Statement
\int_{1}^{e}\frac{dx}{x\sqrt{1+ln^2x}}
The Attempt at a Solution
for u=lnx-->u'=1/x
\int \frac{du}{\sqrt{1+u^2}}
substituting u=tan\theta
=\int \frac{d\theta}{cos\theta}=ln|sec\theta+tan\theta|...
Homework Statement
Find d^2y/dx^2.
y = x cos x
The Attempt at a Solution
I've been doing derivatives recently and now got into doing them with trig functions.
I thought it was,
y = x cos x = -xsinx = -xcosx
but that is the derivative of the derivative.
The problem...
Derivative trigonometric functions
Homework Statement
Find d^{2}x/dt^{2} as a function of x if dx/dt=xsinx
Homework Equations
The Attempt at a Solution
I tried to solve the problem by taking a second derivative of dx/dt=xsinx
but I was not sure how to start. Also, it is...
This is an example from the book. Evaluate
\int {\frac{{\sqrt {9 - x^2 } }}{{x^2 }}dx}
I understand all the steps that get me up to = - \cos \theta \, - \theta \, + C
Then the book goes on to explain:
"Since this is an indefinate integral, we must return to the original variable...
Homework Statement
Three functions are defined as follows:
f:x> cos x for the domain 0< (or equal to) x < (or equal to) 180
g:x> sin x for the domain 0< (or equal to) x < (or equal to) 90
h:x>tan x for the domain p< (or equal to) x < (or equal to) q
Find the range of f.
-1<(or...
\int\sqrt{16-(2x)^{4}}xdx
Hint says you may like to use the identity sin(theta)cos(theta)= sin(2theta)/2
However, I think I found a way to use 1-sin^2(theta)=cos^2(theta)
First, (2x)^4 = 16x^4
So make it 16(1-x^2)^2.
Take the 16 out of the root and the integral and you have...
Homework Statement
Un a sequence
0 < x < pi/2
U0 = 2cosx
Un+1 = quroot( 2 + Un)
1) Calculate U1, U2, and U3 in function of x (simplify maximum)
2) Show that Un = 2cos( x / 2^n)Homework Equations
The Attempt at a Solution
1)
U1 = sqroot( 2 + 2cosx) = sqroot( 2 (1 + cosx))
= ?? (now , how...
Question 1
sin theta = 2/3 tan theta < 0
sin2 theta = ??
how would i do this?
please help
____
Question 2
solve
2cos^2 theta - cos theta = 1 for 0 <= theta < 2pie
how would i do this one too?
Anybody that can show how to deduce
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
From the relations that we get from eulers formula..
Should be really simple but I think that I have got some relations wrong so I need to se the real solution.:rolleyes:
Thanks!
I was doing my exam today and ran into a couple problems.
First one: how do you differentiate \tan^2?
I converted it into \sec^2 - 1 and used the u/v = (u`v - v`u)/v^2 method, but I would like somebody clever to do it for me, just to be sure, please.
Homework Statement
Another problem.
Rate of...
For a homework assignment I'm supposed to prove that sin(x)^2+cos(x)^2=1, using only the following identities (along with algebraic operations):
sin(-x)=-sin(x)
cos(-x)=cos(x)
cos(x+y)=cos(x)cos(y)-sin(x)sin(y)
sin(x+y)=sin(x)cos(y)+cos(x)sin(y)
I can't figure this out, because as far...
more trig...
Amm I've been at this problem for an hour already it loooked really easy but for some reason i can't reach the answer
(tan x + sec x)^2 = (1 + sin x)/(1 - sin x)
soo what went and tried was expand it and then exchage tan and sec..
(sin^2 x /cos^2 x )+ (2/cos x) + (1/ sin^2 x)...
How would one go about solving sin(x) = x/2
I.e. the intersections of
f(x)=sin(x)
&
g(x)=x/2
I can rigorously solve this by going to each individual period and finding the intersections. But is there a better way?
Homework Statement
http://www.jyu.fi/kastdk/olympiads/2004/Theoretical%20Question%203.pdf
http://www.jyu.fi/kastdk/olympiads/2004/Solution%203.pdf
Question A- (b)
They use some trigomentric identity that I don't understand, which one is it?
Thanks in advance.
Homework...
Homework Statement
Prove the following trigonometric reduction using integration by parts:
\int \sin^n x dx = - \frac{\ \sin^{n-1} x \cos x}{n} + \frac{\ n-1}{n} \int \sin^{n-2} x dx
2. The attempt at a solution
I tried using integration by parts by breaking up sin^n x into sin^(n-2) x...
just encountered this question and kinda confused at how to solve it since I havn't bin told and havn't worked it out for myself. hope you can help.
Homework Statement
Use the graphs (shows 2 graphs) to find the values of x in the range 0 /leq x /leq 720 when 2sinx = cosx -1
Homework...
Homework Statement
Compute \int_{0}^{\infty} \frac{\tan x}{x} {} dx
Homework Equations
The Attempt at a Solution
Got no idea, obviously the derivation differs from the \int_{-\infty}^{\infty} \frac{\sin x}{x} {} dx one. The result I'm supposed to get is \frac{\pi}{2} .
Homework Statement
use the inverse functions where necessary to find all solution of the equation in the interval [0,2pi). Use a graphing utility to verify.
2cos(squared)x+3cosx=0
Homework Equations
The Attempt at a Solution
The answer is pi/2 and 3pi/2 from my teacher..
===...
Hey I'm just having trouble with this question
Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65 deg. The component of the longer vector along the line perpendicular to the shorter vector, in the plane of the vectors...
Homework Statement
I can't seem to find online how to calculate the error propogated by trigonometric functions.
That is, I know the uncertainty in \theta but am not sure how to deal with it when I apply the tan function.
I am quite okay with how to deal with all the basic...
Homework Statement
Integral of \int \sin^{11/3}\alpha\, d\alpha
Homework Equations
\sin^2\alpha = 1 - cos^2\alpha
The Attempt at a Solution
\int (\sin^2\alpha)^{4/3}\sin\alpha \, d\alpha
\int (1-cos^2\alpha)^{4/3}\sin\alpha \, d\alpha
u = \cos\alphad
du = \sin\alpha\...
Homework Statement
Prove the following identity: (1 + cos \theta)^2 + sin^2\theta = 2(1 + cos \theta)
Homework Equations
cos^2 \theta + sin^2 \theta = 1
The Attempt at a Solution
I've squared out the first bracket so that it becomes 1 + cos^2 \theta and multiplied out the second bracket so...
Homework Statement
Simplify
The problem is either 1+[(cosx)/2]
or
1+[cos (x/2)]
The first one looks unworkable so I'm going with the second...unless any of you see that the first one looks normal...
Homework Equations
I derived/proved some below...
The Attempt at a...
Greetings my friends:
I have been reading a book about optimization and I found the following trigonometric equation:
tan(10x.pi)= - 10 pi x (this equation goes from x E [-1,2]
it is easy to see that has infinite solutions, but the author came to the conclusion that the solutions are...
Hi. I need to prove the following identity
\arccos{z} =i \ln { z + (z^2 -1)^\frac{1}{2} }
I was given a hint to write
\cos{A}=z,
then rewrite
\cos{A}
in terms of the exponential.
\cos{A}=\frac{\exp{iA}+\exp{-iA}}{2}=z
I took the log on both sides and got stuck at that...
I need to solve
sin(ax)sin(bx) - k cos(ax)cos(bx) = -1
where k > 1 is constant and so are a and b, and they are all irrational.
(It's part of a much larger question in optics...)
Any ideas, please?
Thanks
Hi, all I am new to this site and I was wonder if anyone could help.
I took linear algear algebra last semster and am currently taking statics. I want to know if I can use some of the techniques I learned in linear algebra to solve simtultaneous equations which involve sine or cosines
For...
I just came across a problem that wants you to solve for csc of an angle in radians... However, I'm confused about the answer given.
Here is the problem:
Find the csc when t=-2pi/3, which is equivalent to -120 degrees right?
I got -2sqrt.(3)/3 but the answer in the back is -2sqrt.(3)/2...
I was wondering if someone would be able to help me with the following questions:
-A progessive wave has amplitude 0.40m and wave length 2.0m. At a given times the displacement y=0 at x=0. Calulate the displacement at (a)t=5sec (b) t=0.8sec
-A progessive wave has amplitude 2.5m and a time...