Cosine Definition and 343 Threads

Hi, all I am looking into inverse cosine operations. I have a question like follows: Let x and y be two variables of degrees, how to separate equation arccos(x+y) into an equation that contains x and y separately? Such as arccos(x+y) = f1(...x) + f2(...y)? Thank you very much for your...

Homework Statement Show that \cos x=J_{0}+2\sum(-1)^{n}J_{2n} where the summation range from n=1 to +inf Homework Equations Taylor series for cosine? series expression for bessel function? The Attempt at a Solution My approach is to start from R.H.S. I would like to express all...

Homework Statement Graph the magnitude and phase of the function: H(w) = cos(3w) Homework Equations None The Attempt at a Solution So here's the thing, I understand how to graph the phase and magnitude of any sort of function like X(w) = A*exp(wt). In that case, the magnitude...

I am trying to fit a cosine function to two points knowing that the first is an inflection point (e.g. a trough) and also knowing the gradient at the second. I have a gut feeling this has a unique solution it just needs the right identities and massaging but as of yet I haven't found the way...

Homework Statement Simplify the following expression: arccosh \left(\frac{1}{\sqrt{1 - x^2}}\right) \forall x ∈ (-1, 1) Homework Equations cosh(u) = \left(\frac{1}{\sqrt{1 - tanh^{2}u}}\right) u ∈ ℝ The Attempt at a Solution x = tanhu ∴ u = arctanhx u ∈...

Hello, I am considering the hyperbola x^2-y^2=1 and its intersection with the line y=mx. The positive x-coordinate of the intersection is given by: x=\sqrt{\frac{1}{1-\tan^2\alpha}}=\sqrt{\frac{\cos^2 \alpha}{\cos(2\alpha)}}=\cos\alpha \sqrt{\sec(2\alpha)} where we used the identity...

Hello, I wanted to know why the graph of the hyperbolic cosine function (1/2(e^x)+1/2(e^-x)) looks like a parabola. Is there any reason for this? I suppose the individual exponential functions both go to infinity in a symmetric way... but I wanted a better reason :). Thanks, Mathguy

Homework Statement For my physics EEI, I have developed the formula: g-forces=√(391.88-337.12 cosθ)/9.8 I need to linearise the graph into the form y=mx+c. I'm not sure where just the angle is the independent or cos of the angle. Homework Equations y=k√(x) can be graphed as y vs...

Homework Statement show that xf(x)=integral from 0 to infinity of [B*(w)sin(wx)]dw , // B* is a function not B * w where B* = -dA/dw A(w) = 2/pi integral from 0 to infinity [f(v) cos(wv)] dv Homework Equationsf(x)=integral from 0 to infinity [A(w)cos(wx)] dw The Attempt at a Solution...

State the special cases of the above two formulas for $n = 0, 1,$ and $2$. These should be familiar formulas. I don't see what is so special and familiar about when n = 2 or for cosine n = 1.When $n = 0$, we have $$ \sum\limits_{k = 0}^0\cos k\theta =...

Prove that the $\sum\limits_{k = 0}^n\cos k\theta = \text{Re}\left(\frac{1 - e^{i(n + 1)\theta}}{1 - e^{i\theta}}\right)$ simplifies to $$ \sum\limits_{k = 0}^n\cos k\theta = \frac{\sin\left(\frac{n + 1}{2}\theta\right)}{\sin\frac{\theta}{2}}\cos\frac{n}{2}\theta $$ So I have that the real part...

I was just finishing my physics homework (don't worry this isn't a HW question, the homework is done) and the last calculation I had to do was cos2(θ) = 0.6. I just plugged this into my calculator to solve for me and got it right. Now I'm curious though. How would one solve this by hand?

For part (i), my answer is correct but my answer for (ii) seems to be a little bit out. I can't spot where I've gone wrong. Can anyone help me out? Many thanks. Homework Statement Q. In the given triangle, find (i) |\angle abc|, (ii) |\angle bac|. The Attempt at a Solution (i) cos B =...

Hi, I am working on proofs of the difference identities for sine, cosine, and tangent. I am hoping to solve these using a specific diagram (attached). I was wondering if you could help me with the difference of cosines. Is it possible to derive it using the attached diagram? If so, how...

Homework Statement With a series like: pi^(n/2)*cos(n*pi) How am I meant to approach this? Do I use the Squeeze Theorem? Homework Equations The Attempt at a Solution

While we calculate cross product of two vectors let A and B we write ABsinθ. And while we calculate dot product of them we write ABcosθ. Why particularly we use sinθ for cross product and cosθ for dot product.Is there any physical reason why we choose sine for cross product and cosine for...

Homework Statement Need help with a question ... .__." q: if the magnitude of a=2 and the magnitude of 5a-2b= 7.7, and the angles between the vectors a and b is 50 degrees determine the magnitude of b. Homework Equations The Attempt at a Solution first I drew a diagram...

Homework Statement The Attempt at a Solution So after I have properly extended the series, I want to find the A_n coefficients. In the case of A_0 I get 1/2 -- good, great. That's what the book gets. Now for the general A_n: A_n = \frac{1}{2} \int^2_{-2} (1)cos(\frac{n\pi x}{2})...

sketch the spectrum of the PAM signal S(f) if the input is m(t)=cos(2*pi*fm*t) where fm=3000 at a sampling rate of 10000 using rectangular pulses of duration 0.04ms. in the range +-15Khz S(f)=H(f)*M'(f) taking the Fourier transform of the rectangular pulse we obtain: H(f)=Tsinc(Tf) where...

Question about the "start" of a cosine Fourier series Hey. I was just looking through Paul's Online Notes http://tutorial.math.lamar.edu/Classes/DE/FourierCosineSeries.aspx to teach myself Fourier Series and I had a question about the a_{0} term of the cosine series. In the online lesson...

Homework Statement Synchronous demodulate x(t). Homework Equations xc(t) = cos(2pi*fc*t), fc is the carrier frequency xm(t) = cos(2pi*fm*t), fm is the modulation frequency x(t) = xc(t)*(1+m*xm(t)), m is the modulation index m = .8 fc = 2000 hz fm = 200 hz The Attempt at a Solution I...

I have to draw cosine waves in relation to pattern formation for mathematical biology, for example, I have to plot things similar to these on the x-axis; cos( 2*pi*x / √5 ) from x= 0 to √5 cos( 3*pi*x / 2 √5 ) from x= 0 to 2√5 cos( 3*pi*x / 2 √(5/6) ) from x=0 to 2√5 And with the y-axis; cos(...

Homework Statement Solve for |θ1-θ2| Homework Equations cosθ1 + cosθ2 = 0 sinθ1 + sinθ2 = 0 The Attempt at a Solution This is a silly math problem within a larger question I'm working on. I have solved for it multiple times now using different trig identities and I get different answers...

Homework Statement f(x)= {1, ‐1/2<x≤1/2} {0, ‐1<x≤ ‐1/2 or 1/2<x≤1} State whether or not the function's Fourier sine and cosine series(for the corresponding half interval) converges uniformly on the entire real line ‐∞<x<∞ Homework Equations The Attempt at a Solution...

It's the following one: \displaystyle\lim_{x \to{0}}{\frac{1-\cos(1-\cos x)}{3x^4}} In case we have to apply L'Hospital, appart from it, how could I solve this without it? Thanks!

By continuity I mean an unbroken fractal. With certain variants, one ends up with sharp gaps in the fractal. mag=({x^2+y^2+z^2})^{n/2} yzmag=\sqrt{y^2+z^2} \theta= n *atan2 \;\;(x + i\;\;yzmag ) \phi = n* atan2\;\; (y + iz) new_x= \cos{(theta)}\;*\;mag new_y=...

I am having the hardest time attaching my brain to some sort of method to know when to use sine and cosine on force problems. What is an easy way of remembering which function to use to find the force in the direction of x and force in the direction of y?

Homework Statement find ∫4cosx*sin^2 x.dx Homework Equations The Attempt at a Solution ∫4cos x * 1/2 (1 - cos2x) ∫2cosx - 4cos^2 x. Then i don't know whereto go from here??

Homework Statement find the limit of : \lim_{x\rightarrow0}\frac{\sqrt{5-cos(x)}-2}{x^{2}} Homework Equations The Attempt at a Solution I multiplied the numerator and the denominator by the conjugate of the numerator and i got : \frac{1-cos(x)}{x^{2}(\sqrt{5-cos(x)}+2)} then: i divided...

Homework Statement Problem 8-17 from Mathew's and Walker's book: Use a cosine transform with respect to y to find the steady-state temperature distribution in a semi-infinite solid x>0 when the temperature on the surface x=0 is unity for -a<y<a and zero outside this strip. Homework...

Homework Statement What are the Fourier sine and cosine transformations of exp(5t)? Homework Equations Fc (ω) = (√(2/∏))∫exp(5t)cos(ωt)dt , (between boundaries of infinity and zero) The Attempt at a Solution When I try to integrate by parts I just end up going round in...

Homework Statement a) Find the cosine of the angles that the line r = [-3,2,5] + t [2,2,√2 ] makes with the coordinate axes. b) If a,b and c are the angles that the line makes with the x,y and z axis respectively, find the value of cos^2a + cos^2b + cos^2c. c) What is the magnitude of the...

Homework Statement Homework Equations The Attempt at a Solution I don't see how the textbook gets from step 1 to step 2. If anything, the cosines cancel and the answer should be (sine^2)x

Homework Statement Show that cosh^2(x) = (cosh(2x) - 1)/2 Homework Equations cosh(x) = (e^x + e^-x)/2 The Attempt at a Solution I have attempted this multiple times and get the same results every time. Squaring cosh(x) I get 1/4(e^2x + e^-2x +2), which is i believe 1/4(cosh(2x) +2)...

Homework Statement \frac{d^{2n}}{dx^{2n}}\cos x n \in N Homework Equations \cos x=\sum^{\infty}_{k=0}(-1)^k\frac{x^{2k}}{(2k)!} The Attempt at a Solution \frac{d^{2n}}{dx^{2n}}x^{2n}=(2n)! But k is different that n. I don't have a clue how to solve that.

Vector and cosine law?? Homework Statement Three deer, A, B, and C, are grazing in a field. deer B is located 62m from deer A at an angle of 51 north of west. deer C is located 77 degree north of east relative to deer A. The distance between deer B and C is 95m. What is the distance between...

Suppose that a spaceship is fired into orbit from Cae Canerveral. Ten minutes after it leaves Cape, it reaches its farthest distance north of the equator, 4000 kilometers. Half a cycle later it reaches its farthest distance south of the equator (on the other side of the Earth, of course!), also...

Homework Statement High tide at 4am with a depth of 6 meters. Low tide at 10 am with a depth of 2 meters. Model the problem using the equation to show the depth of the water t hours after midnight. Homework Equations y= A cos(Bx+C) +D The Attempt at a Solution: I am not getting...

Homework Statement So I am a little rusty on my basic math and I am trying to simplify this expression. In case you were curious the expression came from a signal block diagram that I calculated the transfer function H(z) to then found the frequency response H(f) and I think i have done that...

Homework Statement Show that, if n is an odd number, \int_0^\pi \cos^nx dx = 0 Homework Equations The Attempt at a Solution \int_0^\pi \cos^nx dx = \int_0^\pi \cos^{n-1}(x)\cos (x) dx = = \int_0^\pi (\cos^2x)^{\frac{n-1}{2}} \cos x dx = \int_0^\pi (1 - \sin^2x)^{\frac{n-1}{2}} \cos...

Homework Statement Hello! I've run into a problem at work and need a quick solution! Basically I need to work out the cut size of a curved bar. I have the chord length (650mm) and the radius' (1335mm) Obviously i need to calculate the inner most angle, then multiply my diameter by pi, divide...

Hey, If I wanted to make up problems that are solved using the law of cosines, shouldn't it work out even if I arbitrarily choose side a, b, and θ? After all, any two sides and an angle between them form a triangle. Correct?

Can someone give a more intuitive explanation on how it is (if it is true), that; ∫all cos (nx) cos (mx) = 0 if n!=m or ∫all sin (nx) sin (mx) = 0 if n!=m thanks

I know that a proper orthogonal rotation matrix in R^{2} has the form [cos \theta sin \theta -sin \theta cos \theta] which would rotate a vector by the angle \theta. However, I have also seen the matrix [sin \theta cos \theta -cos \theta sin \theta] What type of rotation...

Homework Statement \omega^2=(2/M)\sum_{n>0}\frac{A\sin(nk_0a)}{na}(1-\cos(nKa)) A, a, and k_0 are constants, n is an integer. I need to find \omega^2 and \frac{\partial\omega^2}{\partial K}, but I have no idea where to start.Homework Equations Not sure, the stuff above.The Attempt at a...

Homework Statement Find the Fourier cosine series representation of g(\chi) = \chi (\pi + \chi) on the interval (0,\pi) The attempt at a solution Okay so I've got a0=\frac{1}{\pi}\int\chi(\pi+\chi)d\chi =\frac{5\pi^{3}}{6} an=\frac{1}{\pi}\int\chi(\pi+\chi)cos(n\chi)d\chi for...

Smart people help! Trignometric question. Homework Statement A pedestrian bridge is build over a river. The angle of depression from one end of the bridge to a large rock beside the river is 37°. The distance from that end of the bridge (ptA) to the rock is 112m while the distance from the...

Hello, I was wondering if the cosine of theta, in the work equation, related to the angle of the applied force?

Find two solutions for Cosine theta = 1/2 for... [b]1. Find two solutions for Cosine theta = 1/2 for 0 degrees less than or equal to theta less than or equal to 360 degrees. Express answers in degrees and radians. Homework Equations [b]3. I know that Cosine theta = 1/2 gives you 60...

Homework Statement Two ropes are attached to a log that is floating in the water. A force of 80.0 N is applied to one rope and a force of 60.0 N is applied to the other rope, which is lying at an angle of 40° from the first rope. What is the net force on the log? We know that the angle...