Hello,
Probably a simple problem, but I am not able to figure it out.
a \cos (\epsilon) - b \sin (\epsilon) = c in-phase part
a \sin (\epsilon) - b \cos (\epsilon) = d out-of-phase part
In order to find the phase shift, the in-phase term has to be divided by the out-of-phase...
These are the two last problems I'll bother you with for a short while (I love this forum, I'll definitely stay on and hopefully be able to contribute in the future).
Homework Statement
Problem 1:
(##-x^2##-1)sin2x > 0 , xe[0,2\pi]
Problem 2:
##2^{-x^2+x+2}## < 4
Homework...
Homework Statement
Sketch the curve of y=sin(x)+sin(2x)
I got all the derivatives, and the roots N(k*∏|0), but now I'm stuck with the maxima/minima
Homework Equations
First derivative y'=cos(x)+2cos(2x)
The Attempt at a Solution
I set cos(x)+2cos(2x)=0 but now I'm stuck. I...
I have become stuck while trying to evaluate the following trigonometric integral:
\int_0^{\pi} (A + B \sin x)^n dx.
First, I have tried to find a recurrence with respect to n, from which the closed-form solution could be calculated. However, I have failed to do this. Similarly, my effort to...
Working on some fluid mechanics research for flat plate boundary layer, stuck on this integral:
∫sin(∏y/2δ)dy for 0<y<δ
Any help would be deeply appreciated.
Hello everyone, I've wandered PF a few times in the past but never thought I'd join, here I am, how exciting.
To keep it short I'm trying to understand the proof behind Fourier Series and can't quite get to grips with basic trigonometric orthogonality.
I understand that sin and cos are...
i was thinking hard how to integrate this, but none of the techniques I know did work.
please kindly help with this matter. thanks!
$\displaystyle\int\sqrt{1+\cos\theta}d\theta$
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...
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.
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"?
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
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)...
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...
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)}...
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...
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?:
$$\int \frac{\tan(x)}{x}\;dx$$
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...
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...