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  • trigonometry - when to use sine vs cosine vs tangent - Mathematics . . .
    E g for sin, how many times bigger is the opposite side than the hypoteneuse So, is it correct so assume that if you know one of the angles besides the 90 degree angle and 1 length of one side you can determine the sine, cosine and tangent of that triangle? Strictly speaking, we talk about the sine, cosine and tangent of angles not triangles
  • Is there a way to get trig functions without a calculator?
    In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calc
  • Expressing a combination of sine and cosine as a single cosine
    Prove that: $$\\dfrac{\\sqrt2}2 \\cos \\omega t - \\dfrac{\\sqrt2}2 \\sin \\omega t = \\cos \\left(\\omega t + \\dfrac\\pi4\\right)$$ Obviously, if we are evaluating
  • How were the sine, cosine and tangent tables originally calculated?
    Tables of sines came later in India, then in the Islamic world, then in Europe Tangent tables started in the Islamic world As far as I know there have been no cosine tables, for the good reason that $\cos A=\sin(90^\circ -A)$ And measuring was not used, too imprecise $\endgroup$ –
  • Why use sine and cosine when resolving vectors into components?
    The reason we use sine and cosine is because of the way they are defined for triangles Remember that for an angle $\theta$ in a triangle, \begin{equation*} \sin\theta = \frac{\text{length of opposite side}}{\text{length of hypotenuse}},\quad\cos\theta= \frac{\text{length of adjacent side}}{\text{length of hypotenuse}} \end{equation*}
  • Mnemonic for derivative integral of $\\sin x$ and $\\cos x$
    I know by heart that $\sin$ and $\cos$ can be written in terms of exponents, and that $\cos$ is symmetric and $\sin$ is anti-symmetric So I can immediately remember $$\cos(x)=\frac{e^{ix}+e^{-ix}}{2} $$ Derivative of exponent is very simple and I already know the result, just prefactor is in question
  • Why is the derivative of a sine function a cosine function?
    Notice that $\sin \theta$ has maximums and minimums where $\cos \theta$ has zeroes Similarly, the slopes of the tangent lines of $\sin \theta$ are 1 and -1 precisely where $\cos \theta$ attains those values Now that doesn't explain why $\frac{d}{d\theta} \sin \theta = \cos \theta$ everywhere, but it's a good way to remember the relationship
  • Why do both sine and cosine exist? - Mathematics Stack Exchange
    $\begingroup$ @goblin,Of course your conditions work, since they translate (in words) to "$(\cos(x),\sin(x))$ is the arclength parameterization of the unit circle, starting at $(0,1)$ and moving in the positive direction", which is basically the definition of sine and cosine used most commonly in calculus courses It is not too hard to show





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