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...; \Longrightarrow\; dx=-\sin \theta d\theta\quad\hbox{and}\quad 1-x^{2} =(\sin \theta)^2. =(-1)^{l+1}\int\limits_{\pi}^{0}\left( \sin \theta \right) ^{2l+1} d\theta,

.... Tidus tries to flee, but Auron allows the two of them to be pulled in by Sin. <ref>'''Tidus:''' "Auron! Let's get out of here!" <br /> '''Auron:''' "We' ...eam? <br /> '''Tidus:''' You mean I'm sick? <br /> '''Rikku:''' Because of Sin's toxin, yeah.</ref>

:<math> \psi(x) = a\cos (kx) + b \sin (kx)\ ,</math> :<math> 0=\psi(0)=a\cos(0)+b\sin(0)=a\ .</math>

...a life without committing sin, and thus was a fit sacrifice for humanity's sin, a view known as "[[substitutionary atonement]]". He is also considered to ...ginal sin is inherited; rather, we all freely face the same choice between sin and salvation that Adam and Eve did. Pelagianism was opposed by the Council

\int_{0}^{\pi}\sin\theta\, d\theta \int_0^{2\pi} d\varphi\; R^m_{\ell}(\mathbf{r})^*\; R^m_{\e ...l}^m (\cos\theta) \equiv \left[\frac{(\ell-m)!}{(\ell+m)!}\right]^{1/2} \,\sin^m\theta\, \frac{d^m P_\ell(\cos\theta)}{d\cos^m\theta}, \qquad m\ge 0,

The [[trigonometry|trigonometric functions]] <math>\sin x</math>, <math>\cos x</math>, <math>\tan x</math>, <math>\sec x</math>, <m

h_r = 1, \qquad h_\theta = r, \qquad h_\phi = r\sin\theta \nabla \times \mathbf{F} = \frac{1}{r^2\sin\theta}

...le \mathbb{R}^3</math>, the vector product is a vector with length ''AB'' sin &theta;_AB, where ''A'' is the length of '''A''', ''B'' is the ...\times \mathbf{B} = \mathbf{a}_\textrm{N}\, |\mathbf{A}|\, |\mathbf{B}|\,\sin\theta_{AB},

d\mathbf{S} = r^2\, \sin\theta \, d\theta\, d\phi \, \mathbf{e}_r\quad \hbox{and}\quad \mathbf{E}\cdot d \mathbf{S} = E_r(r) r^2 \sin\theta d\theta d\phi

==Periodicity and relation with [[sin]] and [[cos]] functions== : <math> \exp(\mathrm{i} z) = \cos(z)+\mathrm{i} \sin(z) ~ \forall z\in \mathbb{C} </math>

2T = \mu R^2\big [\dot{\theta}^2+(\dot\varphi\,\sin\theta)^2\big]. H = \frac{1}{2\mu R^2}\left[p^2_{\theta} + \frac{p^2_{\varphi}}{\sin^2\theta}\right].

...s <math>~\mathrm pow( sin(x),a)~</math> or as <math>~\mathrm{pow}_a\big(\sin(x)\Big)~</math>. !-->

sb = sin(beta) sa = sin(alpha)

\frac{1}{\sin \theta}\frac{d}{d\theta} \sin\theta \frac{d}{d\theta}P^{m}_\ell +\left[ \ell(\ell+1) - \frac{m^2}{\sin^2\theta}\right] P^{m}_\ell = 0.

...and ''y'' axis is therefore ''r'' sin&theta;cos&phi; and ''r'' sin&theta;sin&phi;, respectively. In summary, the spherical polar coordinates ''r'', &the x &= r \sin\theta\cos\phi \\

\int^{\pi}_{0} P_{n}(\cos\theta) P_{n'}(\cos\theta) \sin\theta \;d\theta = 0\quad \hbox{for}\quad n\ne n'. \frac{d}{d\cos\theta} \sin^2\theta \frac{d}{d\cos\theta}

...da - \Delta \lambda } - ( f + \Delta f )t \right) \right] </math><math>+ \sin \left[ 2 \pi \left( \frac {x}{\lambda + \Delta \lambda } - ( f - \Delta f ...2 \pi \left( \frac {x} {\lambda_{mod}} - \Delta f \ t \right) \right] \ \sin \left[ 2 \pi \left( \frac {x}{\lambda} - f \ t \right) \right] \ , </mat

#'It's a Sin' (Fred Rose, Zeb Turner) - 2:39

:<math> g = G \left[ 1 + \left(\frac{5}{2} m - f\right) \sin^2 \varphi \right] \ , </math> :<math>g = G \left[ \frac{1+k\sin^2 \varphi}{\sqrt{1-e^2 \sin^2 \varphi }} \right] \ , </math>

d\Omega = r^2\;|\sin(\pi+\theta)|\; d\theta d\phi=r^2\;\sin\theta\; d\theta d\phi, \quad ...pi+\theta)\; d\Omega}{4\pi \epsilon_0 r^2} =\mathbf{n} \frac{P \cos\theta\sin\theta d\theta d\phi}{4\pi \epsilon_0 }.

...ons are '''[[sine]]''' and '''[[cosine]]''', denoted respectively as <math>sin(x)</math> and <math>cos(x)</math>. The other trigonometric functions can be :<math>sin(x) = \frac{e^{ix}-–e^{-ix}}{2i}</math>

0 & 0 & r^2\sin^2\theta \\ 0 & 0 & \frac{1}{r^2\sin^2\theta} \\

:<math>q_1 = \cos \left( \frac{\alpha_1}{2} \right) + u_1 \sin \left( \frac{\alpha_1}{2} \right)</math> :<math>q_2 = \cos \left( \frac{\alpha_2}{2} \right) + u_2 \sin \left( \frac{\alpha_2}{2} \right)</math>

\cos (\beta /2) & \sin(\beta /2)\\ -\sin(\beta /2) & \cos (\beta /2)

...n the confessional of the sin of contraception that this was not a 'mortal sin', and that they need no longer accuse themselves of it if they already have

t=M_PI/4.-z; c=cos(t); s=sin(t); u=1./16./(z*z);

...e equal to 1), has a [[hypotenuse]] of <math>\sqrt{2}</math>. Thus, <math>\sin\left(\frac{\pi}{4}\right) = \cos\left(\frac{\pi}{4}\right)=\frac{1}{\sqrt{2

F_\nu(x) = \frac{1}{\pi} \frac{\sin\nu x}{x}\quad\hbox{with}\quad \int_{-\infty}^{\infty} F_\nu(x)\mathrm{d}x = \frac{2\sin \nu x}{x},

+ (\hat{n} \times \vec{r}\,) \sin\varphi . \vec{r}_\perp \mapsto \vec{r}\,'_\perp = \cos\varphi\;\vec{r}_\perp + \sin\varphi\;(\hat{n}\times\vec{r}\,).

\sin kx , \quad \cos kx \quad \hbox{and}\quad \cos \omega t,\quad \sin \omega t. ...cludes a cosine type solution, so that the spatial equation is of the form sin''kx''. If the string has length ''L'' and its end is also clamped, it follo

...\pi x/T)</math> and so on separately, it is sufficient to have function [[sin]]. In the similar way, it is sufficient to describe the discrete implementa

\dot{x}(t) = - A\omega\sin\omega t x(t) = A\cos\omega t\quad \hbox{and}\quad \dot{x}(t) = -A\omega \sin\omega t

...en by <math>\cos \theta \,</math>, the ''y''-coordinate is given by <math>\sin \theta \,</math> and the gradient of the radius from the centre (0,0) to th

...other Islamic prophets), without material possessions, and abstaining from sin.<ref name=Jesus_abstained_from_sin>III&E, [http://www.islam.tc/alhilaal/sit ...[Damascus]], presently in [[Syria]], once the world has become filled with sin, deception, and injustice; he will then live out the rest of his natural li

...entional Cartesian coordinates by <math>x=r\cos\theta</math> and <math>y=r\sin\theta</math>. In polar coordinates, Laplace's equation is: ...}\frac{\partial \phi}{\partial \theta} = - U\left(1+\frac{R^2}{r^2}\right)\sin\theta</math>

They are [[inverse function]]s of [[Sin]], [[Cos]], [[Tan]] and [[Cot]]

...float: left; margin-left: 50px;"><math> y(a)\cos \alpha - p(a)y^\prime (a)\sin \alpha = 0,</math></div> ..."float: left; margin-left: 50px;"><math> y(b)\cos \beta - p(b)y^\prime (b)\sin \beta = 0,</math></div>

:<math>b \sin \theta = n \lambda \!</math> :<math>I = I_0 \frac{\sin^2 \beta}{\beta^2}, \qquad \beta = \frac{b \pi \sin \theta}{\lambda} </math>

| sin | <math>\sin \theta = \cos \left(\frac{\pi}{2} - \theta \right) \,</math>

|<math>\sin(x)</math> |<math>\textstyle \int_0^x \frac{\sin t}{t} \, dt</math>

\cos\phi & -\sin\phi & 0 \\ \sin\phi & \cos\phi & 0 \\

...ion]], which (denoting their argument as ''x'') are written log(''x'') and sin(''x'') respectively. We shall define these functions and note some of their We see that sin(''x'') is defined for real numbers between, but not equal to either of, 0 a

...r to prove the expression for ''H'', we write, using ''R'' = ''r''&thinsp;sin&alpha; (see the figure), d\vec{\mathbf{s}} \times \vec{\mathbf{r}} = \hat{\mathbf{e}} \,r\sin\alpha\, ds = \hat{\mathbf{e}}\, R\,ds,

* Resistance to a lawful King is sin

...d first taken care to remove his ''flamen'''s cap, for it was considered a sin for a ''flamen'' to wear it at his death.

...{0}^{2\pi} C_\ell^m(\theta, \varphi)^* C_{\ell'}^{m'}(\theta, \varphi) \;\sin\theta\, d\theta \, d\varphi = \delta_{\ell\ell'}\delta_{mm'} \frac{4\pi}{2\ ...l}{\partial\theta} \sin\theta \frac{\partial}{\partial \theta} + \frac{1}{\sin^2\theta} \frac{\partial^2}{\partial\varphi^2}\right].

\cos(z \cos(t)) \sin(t)^{2 \nu} ~t~ \mathrm d t

exec return y s gt sin sort split

:::<math>n\lambda = 2d \sin \theta\,</math>

...ex, it most often treats it as a joyous activity, often with no concept of sin. It even may become a spiritual act, as in [[Robert A. Heinlein]]'s ''[[Str