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\operatorname {crd} \theta =2{\sqrt {\operatorname {haversin} \theta }}} ) Zindler curve (closed and simple curve in which all chords that divide the arc...

{\theta }{360}}} The length of a chord formed with the extremal points of the arc is given by C = 2 R sin ⁡ θ 2 {\displaystyle C=2R\sin {\frac {\theta }{2}}}...

{\displaystyle \theta =2\arcsin {\tfrac {c}{2R}}} The chord length and height can be back-computed from radius and central angle by: The chord length is c...

full circle. Centre: the point equidistant from all points on the circle. Chord: a line segment whose endpoints lie on the circle, thus dividing a circle...

height h {\displaystyle h} . Set the sector crosswise on the added lines at the zero of the outer scale to the half-chord length, c {\displaystyle c} . Find...

{\displaystyle A={\frac {1}{2}}r^{2}\theta .} Using the conversion described above, we find that the area of the sector for a central angle measured in degrees...

{r}}&=r(\theta ){\hat {e}}_{r}\\{\frac {d{\vec {r}}}{d\theta }}&={\frac {dr}{d\theta }}{\hat {e}}_{r}+r{\hat {e}}_{\theta }\\{\frac {d^{2}{\vec {r}}}{d\theta...

\tan \theta ={\frac {\sin \theta }{\cos \theta }},\quad \cot \theta ={\frac {\cos \theta }{\sin \theta }},\quad \sec \theta ={\frac {1}{\cos \theta }},\quad...

the chord VB and the arc VB, is equal to ∆VBQ / 3, also B Q = V Q 2 4 S V {\displaystyle BQ={\frac {VQ^{2}}{4SV}}} . The area of the parabolic sector S...

^{2}\theta +b^{2}\cos ^{2}\theta ,&B_{x}&=-A_{xx}x_{\circ }-A_{xy}y_{\circ },\\[1ex]A_{yy}&=-a^{2}\cos ^{2}\theta +b^{2}\sin ^{2}\theta ,&B_{y}&=-A_{xy}x_{\circ...

area of an annulus sector of angle θ, with θ measured in radians, is given by A = θ 2 ( R 2 − r 2 ) . {\displaystyle A={\frac {\theta }{2}}\left(R^{2}-r^{2}\right)...

bisected chord is the sine of one half the bisected angle, that is, c h o r d   θ = 2 r sin ⁡ θ 2 , {\displaystyle \mathrm {chord} \ \theta =2r\sin {\frac...

in radians: A = R 2 ( θ − sin ⁡ θ ) . {\displaystyle A=R^{2}\left(\theta -\sin \theta \right).} Asymmetric The area of an asymmetric lens formed from circles...

removed. This method uses the properties of chords to establish distance m . sin ⁡ θ {\displaystyle m.\sin \theta } in the top quadrant, and then transfers...

is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane. The hyperbolic angle parametrises...

{\displaystyle r=r(\theta )} expressed in polar coordinates is: A = 1 2 ∫ r 2 d θ . {\displaystyle A={1 \over 2}\int r^{2}\,d\theta .} The area enclosed...

( θ ) sin ⁡ θ {\displaystyle {\begin{aligned}x&=r(\theta )\cos \theta \\y&=r(\theta )\sin \theta \end{aligned}}} For a curve defined by an implicit equation...

circle}}{\text{length of chord}}}={\frac {R}{2R\sin {\frac {\theta }{2}}}}={\frac {1}{2\sin {\frac {\theta }{2}}}}\approx {\frac {1}{2\theta /2}}={\frac {1}{\theta }}} For...

option price for a given change in the underlying benchmark. A major seventh chord in jazz music notation. In genetics, it can stand for a gene deletion (e...

with the cosine and inversine , adapted from the full-chord Greek versions (to the modern half-chord versions). They were described in detail by Aryabhata...

necessarily the standard pitch diameter. Chordal addendum (chordal height) Height from the top of the tooth to the chord subtending the circular thickness arc...