What is $\\sin(\\cos(x))$? - Mathematics Stack Exchange
2015年11月26日 · As the title asks, what is $\sin(\cos(x))$. I want it to be reduced more, if possible. I don't know where to start. I could manipulate the expression in many ways, but none allow me to remove either the $\sin$ or $\cos$. For example:$$\sin(\cos(x))=\sqrt{1-(\cos(\cos(x))^2}$$ Then I'd need to know what $\cos(\cos(x))$ is.
trigonometry - Why $\sin(n\pi) = 0$ and $\cos(n\pi)=(-1)^n ...
$\cdots \sin(-\pi), \sin(0), \sin(\pi), \sin(2\pi), \sin(3\pi),\cdots$ Which is exactly where the sine function has its roots, so it is always equal to $0$. For the cosine case, use the identity $\cos(x) = \cos(x + 2\pi) $ (period of the cosine function is $2\pi$) and plug $\cos(0)$ and $\cos(\pi)$ to …
What is the integral of $\\sin(\\cos x)$? - Mathematics Stack …
2014年12月2日 · What is the integral of $\sin(\cos x)$ ? 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.
When is $\\sin(x) = \\cos(x)$? - Mathematics Stack Exchange
2016年8月28日 · 1) $\cos^2 x + \sin^2 x = 1$ So $2 \cos^2 x = 1$ So $\cos x = \sin x = \pm \sqrt{\frac 12}$ 2) $\sin x$ is the adjacent side of a right triangle.
trigonometry - when to use sine vs cosine vs tangent
2014年2月14日 · If $\tan x$ is known, then $\cos x=\dfrac1{\sqrt{1+\tan^2x}}$ and $\sin x=\dfrac{\tan x}{\sqrt{1+\tan^2x}}$ . Basically, given Pythagoras' theorem , if we know the ratio between any two sides, the other two ratios soon follow.
trigonometry - How can we sum up $\sin$ and $\cos$ series when …
$\begingroup$ @onepound: The big right triangle (with "trigonography.com" along its hypotenuse) has a hypotenuse length of $\sin n\theta/\sin\theta$.
Intuitive understanding of the derivatives of $\\sin x$ and $\\cos x$
r(t) * r'(t) = 0 < cos(t), sin(t) > * < -sin(t), cos(t) > = 0 ( cos(t) * -sin(t) ) + ( sin(t) * cos(t) ) = 0 -sin(t)cos(t) + sin(t)cos(t) = 0 0 = 0 Life is good. If we assume that the definition of cos(t) is -sin(t) and that the definition of sin(t) is cos(t), we find physical behavior exactly like expected: a constant velocity that is always ...
Expressing a combination of sine and cosine as a single cosine
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Easy way of memorizing values of sine, cosine, and tangent
2015年12月1日 · 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
Why use sine and cosine when resolving vectors into components?
2017年5月7日 · 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.
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