What is Sine/cosine: Definition and 15 Discussions

In mathematics, the Fourier sine and cosine transforms are forms of the Fourier integral transform that do not use complex numbers. They are the forms originally used by Joseph Fourier and are still preferred in some applications, such as signal processing or statistics.

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  1. E

    I finding resultants using sine/cosine law

    I need help finding the resultant with vectors: 37.5N[NE] and 45N[21° S of E] I just don't know a way to find the angles within this triangle to help me get the resultant, so can anybody help me out?
  2. tanaygupta2000

    Proof of Parseval's Identity for a Fourier Sine/Cosine transform

    Can anyone help me with the Proof of Parseval Identity for Fourier Sine/Cosine transform : 2/π [integration 0 to ∞] Fs(s)•Gs(s) ds = [integration 0 to ∞] f(x)•g(x) dx I've successfully proved the Parseval Identity for Complex Fourier Transform, but I'm unable to figure out from where does the...
  3. S

    How to write the complex exponential in terms of sine/cosine?

    I apologize in advance if any formatting is weird; this is my first time posting. If I am breaking any rules with the formatting or if I am not providing enough detail or if I am in the wrong sub-forum, please let me know. 1. Homework Statement Using Euler's formula : ejx = cos(x) + jsin(x)...
  4. N

    B Sine/Cosine behaving like a linear function

    Hello all. After completing a problem in which we derived the formulas for potential and spring force energy as functions of time, with simple harmonic motion I noticed the equations are EXACTLY the same, but with sine and cosine switched. The equations were: A sin^2(pi * t) A cos^2(pi * t) I...
  5. B

    Sine/cosine function and polynomial function

    Some values of sine and cosine can ben expressed how the root of a polynomial of nth degree. Example:http://www.wolframalpha.com/input/?i=cos%28%28180%2F7%29%C2%B0%29 (Roll the scroll still you find: "alternate forns" and see the associated polynomial: " x³ - 4 x² - 4 x + 1") So, where I can...
  6. Adriane

    I'm having trouble creating my own trig function

    I'm developing my own trigonometric function concerning a "real world" problem of my choosing. I decided to go with the orbit of Neptune around the sun. I just don't know how to develop the equation itself, like if it would be sine or cosine? I'm just lost as to where to begin. If anyone can...
  7. A

    Can Anyone Help Me Understand Wave Motion for IIT JEE Exam Preparation?

    Hello, I am preparing for the IIT JEE exam, The toughest entrance exam in the Indian subcontinent, and i am struck in confusion about the theory regarding waves in Physics. The problem is that I can;t visualize the sine-cos functions physically , as I could visualize the movement of pulley...
  8. N

    Do we know what radio waves look like?

    A thought occurred to me In precalculus class. At the moment we are learning about sin/cos/tan/cot/sec/csc and their amplitude, periods and phases shifts. I've studied electronics on and off for about a year. I would like to know if we actually know what radio waves look like? do they actually...
  9. B

    How to Determine Where a Sine/Cosine Graph Intersects the X-Axis

    Hi... I'm learning how to graph sine and cosine functions, and I can't seem to figure out how to determine where the line intersects the x-axis? I think I understand how to shift up/down and to the right/left, as well as amplitude and period, but can't understand where to intersect. Can anyone...
  10. O

    Calculating Box Mass Using Normal Reaction Force and Inclined Angle

    Homework Statement A box is held at rest on a smooth slope. The slope is inclined at an angle of 18◦ to the horizontal. Given that the normal reaction force between the box and the slope is 79 N, what is the mass of the box? Homework Equations none The Attempt at a Solution...
  11. E

    Limit as x -> infinity of a sine/cosine graph.

    Homework Statement Lim [2 + 3x + sin(x)] / [x + 2cos(x)] (x->infinity) Homework Equations The Attempt at a Solution My roommate asked me to help him solve this homework question, at first glance I noted the derivative to be: [3 + cos(x)] / [1 - 2sin(x)]...
  12. M

    Sine/Cosine Addition Formulae

    Homework Statement 1, Express x = 3sin3t + 5cos3t in the form of x=Rsin(3t + ø) 2, Express x = 2sin(0.5t + 3) + 3cos(0.5t + 1) in the form x = Rsin(0.5t + ø) All working must be done in radians. Homework Equations Sine and Cosine Addition Formulae sin(A + B) = sinAcosB +...
  13. E

    Creating a 90 Degree Phase Shift with a Sine Wave

    I have a sine wave. i want to make it 90 degrees out of phase. if i remember correctly i could use a capacitor to create a phase lag of 90 degrees (like on of those motors where they put a capacitor to create the offset so it starts to turn) Do you put the capacitor in series? What value...
  14. M

    Understanding the Laws of Sine and Cosine

    Law of Sine = Sin A/a = Sin B /b = Sin c/c Law of Cosines a^2=b^2 + c^2 - 2bc Cos A I used to know how to "prove" both of these laws but I haven't touched math for years. Can someone "prove" them or "explain" what these laws exactly mean?
  15. W

    Sine/cosine sum and difference formulas

    How to proove those formulas for any angle? So far all the proofs I've found are for angles between 0 and 2pi...