What is $\\sin(\\cos(x))$? - Mathematics Stack Exchange
Nov 26, 2015 · 1. You could expand it in a power series. That would give you a good way to approximate it to whatever accuracy you like. A power series around x = 0 has a bunch of sin(1)'s and cos(1)'s which are hard to evaluate but at x = π / 2 the power series expansion is − (x − π / 2) + (1 / 3)(x − π / 2)3 − (1 / 10)(x − π / 2)5 + ⋯ ...
What is the integral of $\\sin(\\cos x)$? - Mathematics Stack …
Dec 2, 2014 · So glad you asked ! :-) Although the indefinite integral does not possess a closed form, its definite counterpart can be expressed in terms of certain special functions, such as Struve H and Bessel J. ∫ π 2 0 sin(sin x) dx =∫ π 2 0 sin(cos x) dx = π 2H0(1) ∫ 0 π 2 sin (sin x) d x = ∫ 0 π 2 sin (cos x) d x = π 2 H 0 (1) ∫ π 2 0 ...
trigonometry - How does a calculator calculate the sine, cosine ...
Calculators either use the Taylor Series for $\sin / \cos$ or the CORDIC algorithm. A lot of information is available on Taylor Series, so I'll explain CORDIC instead. The input required is a number in radians $\theta$, which is between $-\pi / 2$ and $\pi / 2$ (from this, we can get all of the other angles).
trigonometry - when to use sine vs cosine vs tangent
Feb 14, 2014 · However it's a lot easier to find them directly given a standard right-angled triangle problem. For reference, the identities that you can use are: sin2 x +cos2 x tan2 x + 1 1 +cot2 x = 1 =sec2 x, where sec x = 1/ cos x =cosec2x, where cot x = 1/ tan x,cosecx = 1/ sin x sin 2 x + cos 2 x = 1 tan 2 x + 1 = sec 2 x, where sec x = 1 / cos x 1 ...
Easy way of memorizing values of sine, cosine, and tangent
Dec 1, 2015 · Drawing Sin Cos Tan Table. Step 5(orange):Once you have values for sine function, invert them for cosine i.e( sin 90 = cos 0, sin 60 = cos 30, sin 45 = cos 45 and so on) and you get values for cosine function. Step 6: For tangent, put sin/cos values and simplify. Step 7: You can extend the table for further angles by using formulas such as
When is $\\sin(x) = \\cos(x)$? - Mathematics Stack Exchange
Aug 28, 2016 · Hint: Take the equation sin(x) = cos(x) and divide both sides by cos(x) to get tan(x) = 1. Alternatively, using a sum-to-product formula, we can observe that sin(x) − cos(x) = √2sin(x − 45 ∘) Share. Cite. answered Aug 27, 2016 at 21:35. Ben Grossmann. 229k 12 176 342.
algebra precalculus - What do sine, tan, cos actually mean ...
Jul 26, 2015 · The trigonometric functions relate an angle to a length. More precisely, in a rectangle triangle, the sine, cosine and tangent of an angle are the ratio of two of the sides. cos(θ) = x r, sin(θ) = y r, tan(θ) = y x. For convenience, we will now assume that r = 1, as this doesn't change the proportions.
Why use sine and cosine when resolving vectors into components?
May 7, 2017 · The vector is the diagonal of a unique rectangle. The horizontal and vertical components of the vector are by definition the horizontal and vertical sides of the rectangle; that's just the statement that moving from the origin to the endpoint along the ray gives the same ending location as moving only horizontally and then only vertically along those sides.
How to prove Euler's formula: $e^{it}=\\cos t +i\\sin t$?
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sincos implementation - Mathematics Stack Exchange
May 3, 2017 · 0. There's always sin(x) = √1 − cos(x)2 and vice versa that allows you to compute one and compute the other with a square root. However, both glibc and musl libc actually just use two separate calls to sin and cos because the above square root has rounding errors around x = 0. Modern CPUs often have a dedicated sincos instruction that ...