Hi, everyone, I am mathstkk, I am new to the Physics Forum, but I think, at my first sense, this forum is going to be helpful to me^^
Recently, I met one problem about matrix.
The problem is as follow:
Show that the matrix below has NO non-trivial solution if a+b+c=0
The matrix is
1...
Solve for \theta
20= 32[sin\theta] (72/32[cos\theta]) + 1/2(-9.8){(72/32[cos\theta]}2I'm really having trouble with this question. I've tried it many times, but keep getting stuck.
Is there anyway to let X=72/32[cos\theta] and then solve for x with the quadratic equation?
Can someone help me...
Homework Statement
\int sin^2x cos^4x dx
Homework Equations
The Attempt at a Solution
tried:
sin2x formula
writing 1-cos^2 instead of sin^2x
letting u=sinx
letting u=cosx
no luck yet
Homework Statement
Can some one please give me the proof or somewhere I can find the proof or just an explanation why
Sin(-theta) = -Sin(theta
Cos(-theta) = cos(theta)
Tan(-theta)= -Tan(theta)
Thank you..
Homework Equations
The Attempt at a Solution
Homework Statement
prove that, (cos(3x) - cos (7x)) / (sin(7x) + sin(3x)) = tan(2x)
prove that, cos(3x) = 4cos^3(x) - 3cos(x)
Homework Equations
tan(x) = sin(x)/cos(x) must come into the first one
The Attempt at a Solution
tried seperating the fraction so there is only one...
This is a problem from a quiz I had awhile ago, I got the answer correct, but I'm reviewing for a test and I completely forget how I did it. Can someone please show me what I did?
sec4x=2
secx=2
x=π/3 + 2nπ ---> x=π/12+2nπ/4
x=5π/3 + 2nπ ---> x=5π/12+2nπ/4
π=pi
p.s. I mostly just forget how...
Homework Statement
\cos (\frac{(-1)\pi x}{L})-\cos (\frac{3\pi x}{L})
Homework Equations
The Attempt at a Solution
the first cosine is the same as positive but is the second cosine simply equal to
\cos (\frac{\pi x}{L})?
thanks!
Please help me to confirm, weather the following step is correct
|\gamma| \leq \cos (\beta)
\arccos (|\gamma|) \leq \beta
does taking the arccos() on both sides of equation changes the relational operator??
Homework Statement
1)
lim sin^2(3x)/x^2
x->0
2) lim 2sin5x/(3x-2tan2x)
x->0
Homework Equations
lim sinx/x = 1
x->0lim tanx/x = 1
x->0
The Attempt at a Solution
We just began working with limits, and we haven't covered much of trig functions at all, but our prof gave us...
while solving trigonometric equations many times we get answer in different forms depending on the way in which we solve the problem , so what is the best way to ascertain that all the answers are the same ??
pl. help!
Homework Statement
Which of the following is not a possible solution of
0=sinθ+cosθtan^2θ?
A. 3pi/4
B. 7pi/4
C. 2pi
D. 5pi/2
Homework Equations
All trigonometric identities.
The Attempt at a Solution
Too much to write down, at least two pages long, but I've been trying to...
Homework Statement
Find the limit of sin(1/x) as x -> 0, I don't really understand why there isn't a limit, wouldn't it be +/- 1? or it doesn't exist because there are two values? I just need a more thorough explanation of the answer really.
Homework Statement
Calculate the integral \int\limits_0^{\infty} \cos{x^2} dx
This is the exercise from complex analysis chapter, so I guess I should change it into a complex integral somehow and than integrate. I just don't know how, since neither substitution cos(x^2) = Re{e^ix^2} nor...
I'm reading through a solution to a problem and at one point the following identity is used:
\frac{1-\cos(\beta)}{\sin(\beta)}=\frac{\sin(\frac{\beta}{2})}{\cos(\frac{\beta}{2})}
I've been trying to figure out where this comes from but with haven't got it yet.
Any ideas?
I've read a bit about constructibe polygons, and that a regular n-gon can be constructed with compass and straightedge if and only if trigonomatric functions of 2π/n can be expressed with square roots and basic arithmatic alone.
That is possible if and only if n is the product of distinct Fermat...
Hey guys. How are you all doing? I'm helping my younger brother out with his trigonometry homework. He is dealing with verifying trigonometric identities. However, he has the problem that I am getting nowhere with. Hope you all can help. Thanks in advance. :)
Homework Statement
Verify...
Homework Statement
http://d.imagehost.org/view/0659/Capture
Link to wolfram alfa:http://www.wolframalpha.com/input/?i=integrate%28cos%28e^x%29*e^x
What i don't understand is why whey do it like this and why i can't integrate by parts in this case?
Thanks for any replies!
Hello,
What's the easiest way to evaluate an integral like this?
\int_{\frac{-\pi}{2}}^{0}\cos^{10}x dx
The only method I can think of is to expand the \cos^{10} x using trigonometric identities, and getting \frac{1}{32}\left(1-\cos2x\right)^5.
I tried subbing u=1-\cos2x but I doesn't seem to...
Homework Statement
find the dy/dx
of y = Sin4 x2 - Cos4 x2
Homework Equations
derivatives and identities
factoring
dy/dx (Sinx) = Cosx
dy/dx (Cosx) = -Sinx
The Attempt at a Solution
y = (Sin2 x2 - Cos2 x2) (Sin2 x2 + Cos2 x2)
im stuck at this part i don't know how to...
Homework Statement
y=(sin2x)(cos2)
Homework Equations
Product Rule for Derivatives
identities:
derivatives of
Sinx = Cosx
Cox = -Sinx
The Attempt at a Solution
i used the product and chain rule for derivatives then do the identities
y = sin2x*cos2x
dy/dx = (Cos2x)(2)...
Homework Statement
\int_0^1 \! 7x\sqrt{x^2+4} dxHomework Equations
The Attempt at a Solution
Noticing that the radical is of the form x^2 + a^2, I know to use a*tan\theta.
x = 2tan\theta
dx = 2sec^2\theta d\thetaThen I simplified the radical to put it in terms of a trig function...
Homework Statement
\int \frac{4}{x^{2}\sqrt{81-x^{2}}} dx
Homework Equations
The Attempt at a Solution
Since the radical is of the form a^2-x^2, I'm using the substitution x=asin\theta.
x = 9sin\theta
dx = 9cos\theta d\theta
Using this x value, I solved the radical...
This is supposed to be a proof of trigonometric multiplication of complex numbers:
What happened at the =...= point? I understand everything up to that.
Homework Statement
\int sin^6(x)cos^3(x) dx
Homework Equations
cos^2(x) = 1-sin^2(x)
The Attempt at a Solution
Since cos has an odd power, I took one out to make it cos^2(x), which can be used in the identity above.
\int sin^6(x)cos^3(x) dx
\int sin^6(x)(1-sin^2(x))cos(x) dx...
Hello,
I have been an avid reader of the physics forum, and now I think I finally have something worth asking. The problem is engineering-related, but it all comes down to a trigonometric equation, so I'm posting in general math.
The problem is the following:
\frac{1}{N^2}...
Here's the equation:
∫(sqrt(2),2) (1/(x^3*sqrt(x^2 - 1))
I have the entire indefinite integral worked down to this (using x = a*secø):
ø/2 + 1/4 * sin2ø
Now I have the answer book, so I know that's right so far. What I don't understand is how it converted the points of the integral...
Homework Statement
Find the second derivative (y") of y=xtanx.
The attempt at a solution
I got the first derivative (y')
y=xtanx
y'=x(secx)+tanx
I started the second derivative and got stuck
y"=xsec^2x+tanx
Is there any general and hopefully 'easy' way to find the trigonometric ratios of any angle? That is without using the sin, cos etc tables?
If not any angle ... atleast whole number angles?
Homework Statement
prove the identity.
ln csc(x) = -ln sin(x)
The Attempt at a Solution
With a calculator I am able to prove it is in fact an identity, but I have NO clue why? In fact I am quite unclear on logarrithms in general as my algebra class just barely covered them and...
Homework Statement
Find the limit as x approaches zero of xcsc4x = the numerator over cos17x = the denominator
Homework Equations
The Attempt at a Solution
I don't know how to start except maybe multiplying both numerator and denominator by 4
I have been having lots of trouble verifying trigonometric identities. I know the fundamental identities but I am actually having trouble with the algebra that goes along with the problems.
The problem I am working on now is:
cos(x)-tan(x)/sin(x)cos(x) = csc^2 (x) - sec^2 (x)
(The csc...
Homework Statement
lim (sin 2x)/(sin 5x)
x->0
Could someone please help me get started, I simply can't figure this one out.
Homework Equations
The Attempt at a Solution
Homework Statement
Evaluate the definite integral of function dx/x^2+1 on interval [tan(3), tan(6)]
Homework Equations
The Attempt at a Solution
The trigonometric inverse function for dx/x^2+1 is arctanx+c.
I plugged in tan(3) and tan(6), and subtracted arctan(tan(3)) from...
Trigonometric substitution - Why?
Hey guys
Im sitting here with trigonometric substitution problems, and I have a kind of a problem.
I can't see WHY it is legal to substitute x for a sin (\theta)
If you have a the integral:
\int\frac{1}{\sqrt{1-x^2}}dx
Then I know the substitution would...
Hi,
I am seeking some input for an integral I have been stumped on for a few days.
This is the integral:
[(a^2 - s^2)^1/2]/(x-s) ds evaluated over the bounds from -a to a. The symmetry of the integration area allows the integral to be evaluated from 0 to a, and doubled.
I have always...
Homework Statement
I want to express sin(x) in terms of tan(x).Homework Equations
tan(x)=sin(x)/cos(x)
1+tan2(x)=sec2(x)The Attempt at a Solution
sin(x)=cos(x)tan(x)
At this point I realize this is assuming x\neq \pi/2+k\pi
cos^2(x)=\frac{1}{1+tan^2(x)}
therefore...
Homework Statement
I'm trying to integrate the following form:
y = \int e^{\sin x} dx
The Attempt at a Solution
I thought about trying to write something like:
y = \int e^{\frac{i}{2}e^{-ix} - \frac{i}{2}e^{ix}} dx
But this seems to lead down the road of trying to integrate...
I got these two questions wrong and I'm wondering what i did wrong.
Homework Statement [/b]
1. http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q3.jpg
2. http://i324.photobucket.com/albums/k327/ProtoGirlEXE/q4.jpg
The attempt at a solution[/b]
1...
Homework Statement
I got this expression while solving a problem.
(y+1)/(y-1)=sin2x/sin2a
we need to find the range of y
Homework Equations
The Attempt at a Solution
here y=(sin2x+sin2a)/(sin2x-sin2a)
Numerator of RHS lies between sin2a-1 and 1+sin2a
Denominator lies...
Hi. I'd like to know whether is it possible to do the following, and if so, how...(and also, whether is it possible to solve similar problems)
I have parametric equation of a curve and I need to find its intersection with a ray that starts at the origin of the coordinate system and makes...
Homework Statement
(Sin 2θ / sinθ) - (cos 2θ/ cos θ) = Sec θ
just trying to match one side to the other
Homework Equations
all trig identities
The Attempt at a Solution
broke down sin2θ into 2sinθ cosθ then reduced the sinθ in the denominator
giving me
sinθ cosθ -...
Homework Statement
Solve (1+cosx)sin^2x = x^2 + 1/(x^2)
Homework Equations
The Attempt at a Solution
RHS is always greater than or equal to 2
LHS is always less than or equal to 2 as
1+cosx is always less than or equal to 2 and sin^2x is always less than or equal to 1
so...
Homework Statement
The general solution of sinx.siny=1 is
1.x=n(pi)+(pi/2)(-1)^n+1 y=m(pi)+(pi/2)(-1)^m+1
2.x=(4n+1)(pi/2) y=(4m+1)(pi/2)
3.x=(4n-1)(pi/2) y=(4m-1)(pi/2)
where n,m belong to I
Homework Equations
Answer- 2 and 3
The Attempt at a Solution
This is...
Homework Statement
Hey guys, having a trig brain fart here, can you point me in the direction of simplifying:
\frac{6cos\vartheta}{2sin\vartheta-3cos\vartheta}
or is it as simplified as it gets? \
Homework Equations
Thought about using double angle formula
The Attempt at a...
Homework Statement
Is there a way to determine the period of a function like f(x) = a*sin(b*x)^2 + c*cos(d*x)^2 + e*sin(f*x) + g*cos(h*x)?
Homework Equations
The Attempt at a Solution
I know how to find the periods of sines, cosines, and arbitrary sums of the two, but the...