• Thumbnail for Cos-B
    COS-B was the first European Space Research Organisation (ESRO) mission to study cosmic gamma ray sources. COS-B was first put forward by the European...
    3 KB (191 words) - 13:37, 26 November 2022
  • Thumbnail for Law of cosines
    Law of cosines (redirect from Cos law)
    b 2 − 2 a b cos ⁡ γ , a 2 = b 2 + c 2 − 2 b c cos ⁡ α , b 2 = a 2 + c 2 − 2 a c cos ⁡ β . {\displaystyle {\begin{aligned}c^{2}&=a^{2}+b^{2}-2ab\cos \gamma...
    35 KB (5,606 words) - 22:31, 26 March 2024
  • "∓" sign: cos ⁡ ( A ± B ) = cos ⁡ ( A ) cos ⁡ ( B ) ∓ sin ⁡ ( A ) sin ⁡ ( B ) {\displaystyle \cos(A\pm B)=\cos(A)\cos(B)\mp \sin(A)\sin(B)} which represents...
    12 KB (1,635 words) - 22:52, 5 April 2024
  • Thumbnail for Pauli matrices
    manifestly, cos ⁡ c = cos ⁡ a cosb − n ^ ⋅ m ^ sin ⁡ a sin ⁡ b   , {\displaystyle \cos c=\cos a\cos b-{\hat {n}}\cdot {\hat {m}}\sin a\sin b~,} the spherical...
    45 KB (7,421 words) - 11:43, 22 March 2024
  • Thumbnail for Tangent half-angle formula
    a\cos b+\cos a\sin b+\sin a\cos b-\cos a\sin b\\[5mu]&\quad =2\sin a\cos b\\[15mu]&\cos(a+b)+\cos(a-b)\\[5mu]&\quad =\cos a\cos b-\sin a\sin b+\cos a\cos...
    14 KB (3,045 words) - 02:16, 10 April 2024
  • Thumbnail for Spherical trigonometry
    {\begin{aligned}\cos a&=\cos b\cos c+\sin b\sin c\cos A\\&=\cos b\ (\cos a\cos b+\sin a\sin b\cos C)+\sin b\sin C\sin a\cot A\\\cos a\sin ^{2}b&=\cos b\sin a\sin b\cos...
    40 KB (5,837 words) - 21:33, 9 April 2024
  • Thumbnail for Spherical law of cosines
    cos⁡c=cos⁡acos⁡b+sin⁡asin⁡bcos⁡C{\displaystyle \cos c=\cos a\cos b+\sin a\sin b\cos C\,} Since this is a unit sphere, the lengths a, b, and c are simply equal to the angles...
    12 KB (1,951 words) - 01:36, 14 February 2024
  • Thumbnail for Galactic coordinate system
    sin ⁡ ( b ) + cos ⁡ ( δ NGP ) cos ⁡ ( b ) cos ⁡ ( l NCP − l ) cos ⁡ ( δ ) sin ⁡ ( α − α NGP ) = cos ⁡ ( b ) sin ⁡ ( l NCP − l ) cos ⁡ ( δ ) cos ⁡ ( α −...
    14 KB (1,388 words) - 04:59, 5 April 2024
  • Thumbnail for Pythagorean theorem
    b, c, the relation between the sides takes the form: cos ⁡ c R = cos ⁡ a R cosb R . {\displaystyle \cos {\frac {c}{R}}=\cos {\frac {a}{R}}\,\cos {\frac...
    92 KB (12,548 words) - 05:59, 17 April 2024
  • Thumbnail for Haversine formula
    cosines: cos ⁡ ( c ) = cos ⁡ ( a ) cos ⁡ ( b ) + sin ⁡ ( a ) sin ⁡ ( b ) cos ⁡ ( C ) . {\displaystyle \cos(c)=\cos(a)\cos(b)+\sin(a)\sin(b)\cos(C).\,} As...
    18 KB (2,624 words) - 07:32, 9 April 2024
  • Thumbnail for Acute and obtuse triangles
    a\cos ^{3}A+b\cos ^{3}B+c\cos ^{3}C\leq {\frac {abc}{4R^{2}}}} and: p.155, #S25  cos3⁡A+cos3⁡B+cos3⁡C+cos⁡Acos⁡Bcos⁡C≥12.{\displaystyle \cos ^{3}A+\cos...
    13 KB (1,984 words) - 02:15, 9 October 2023
  • Thumbnail for Law of sines
    A&=1-\left({\frac {\cos a-\cos b\,\cos c}{\sin b\,\sin c}}\right)^{2}\\&={\frac {\left(1-\cos ^{2}\!b\right)\left(1-\cos ^{2}\!c\right)-\left(\cos a-\cos b\,\cos c\right)^{2}}{\sin...
    24 KB (3,354 words) - 18:06, 8 March 2024
  • Thumbnail for Triangle center
    reference △ is acute:cos⁡A :cos⁡B :cos⁡Cif ∡A is obtuse:cos⁡A+sec⁡Bsec⁡C:cos⁡B−sec⁡B:cos⁡C−sec⁡Cif ∡B is obtuse:cos⁡A−sec⁡A:cos⁡B+sec⁡Csec⁡A:cos⁡C−sec⁡Cif ∡C is...
    32 KB (3,767 words) - 01:48, 29 March 2024
  • Thumbnail for Quadrilateral
    = ( a c + b d ) ( a d + b c ) − 2 a b c d ( cosB + cos ⁡ D ) a b + c d {\displaystyle p={\sqrt {\frac {(ac+bd)(ad+bc)-2abcd(\cos {B}+\cos {D})}{ab+cd}}}}...
    47 KB (6,758 words) - 15:09, 8 April 2024
  • Thumbnail for Astronomical coordinate systems
    α G ) cos ⁡ ( δ ) = cos ⁡ ( b ) sin ⁡ ( l NCP − l ) cos ⁡ ( α − α G ) cos ⁡ ( δ ) = sin ⁡ ( b ) cos ⁡ ( δ G ) − cos ⁡ ( b ) sin ⁡ ( δ G ) cos ⁡ ( l NCP...
    28 KB (3,948 words) - 03:55, 7 April 2024
  • Thumbnail for John Napier
    sin⁡a=tan⁡(π/2−B)tan⁡b=cos⁡(π/2−c)cos⁡(π/2−A)=cot⁡Btan⁡b=sin⁡csin⁡A.{\displaystyle \sin a=\tan(\pi /2-B)\,\tan b=\cos(\pi /2-c)\,\cos(\pi /2-A)=\cot B\,\tan b=\sin...
    31 KB (3,964 words) - 09:56, 1 April 2024
  • Thumbnail for Euler line
    trilinears cos⁡A+cos⁡Bcos⁡C:cos⁡B+cos⁡Ccos⁡A:cos⁡C+cos⁡Acos⁡B,{\displaystyle \cos A+\cos B\cos C:\cos B+\cos C\cos A:\cos C+\cos A\cos B,} corresponding...
    18 KB (2,403 words) - 01:31, 7 May 2023
  • ( − cos ⁡ t ) + 2 B 0 sin ⁡ t + 2 ( 2 B 0 t + B 1 ) cos ⁡ t + ( B 0 t 2 + B 1 t ) ( − sin ⁡ t ) ] + [ ( A 0 t 2 + A 1 t ) cos ⁡ t + ( B 0 t 2 + B 1 t...
    10 KB (1,812 words) - 07:52, 23 October 2022
  • Thumbnail for Right triangle
    B {\displaystyle B} are complementary. cos ⁡ A cosB cos ⁡ C = 0. {\displaystyle \cos {A}\cos {B}\cos {C}=0.} sin 2 ⁡ A + sin 2 ⁡ B + sin 2 ⁡ C = 2....
    18 KB (2,951 words) - 21:06, 17 April 2024
  • Thumbnail for Ecliptic coordinate system
    by x = r cosb cos ⁡ l y = r cosb sin ⁡ l z = r sin ⁡ b {\displaystyle {\begin{aligned}x&=r\cos b\cos l\\y&=r\cos b\sin l\\z&=r\sin b\end{aligned}}}...
    14 KB (1,331 words) - 17:44, 18 April 2024
  • Thumbnail for Incircle and excircles
    I ) = c sin ⁡ B 2 cos ⁡ C 2 = b sin ⁡ C 2 cosB 2 . {\displaystyle d(A,I)=c\,{\frac {\sin {\frac {B}{2}}}{\cos {\frac {C}{2}}}}=b\,{\frac {\sin {\frac...
    34 KB (5,676 words) - 05:56, 10 March 2024
  • a cosbcos ⁡ a sin ⁡ b cos ⁡ γ ) 2 + ( sin ⁡ b sin ⁡ γ ) 2 cos ⁡ a cosb + sin ⁡ a sin ⁡ b cos ⁡ γ , α = arctan ⁡ sin ⁡ a sin ⁡ γ sin ⁡ b cos ⁡...
    23 KB (3,640 words) - 19:27, 10 January 2024
  • Thumbnail for Sideband
    \cos(A)} to both sides: cos⁡(A)⋅[1+cos⁡(B)]=12cos⁡(A+B)+cos⁡(A)+12cos⁡(A−B){\displaystyle \cos(A)\cdot [1+\cos(B)]={\tfrac {1}{2}}\cos(A+B)+\cos(A)+{\tfrac...
    9 KB (1,248 words) - 21:24, 27 September 2023
  • Thumbnail for Altitude (triangle)
    = cos ⁡ A − sin ⁡ B sin ⁡ C : cosB − sin ⁡ C sin ⁡ A : cos ⁡ C − sin ⁡ A sin ⁡ B , {\displaystyle {\begin{aligned}&\sec A:\sec B:\sec C\\&=\cos A-\sin...
    27 KB (3,754 words) - 09:22, 12 April 2024
  • Thumbnail for Supergalactic coordinate system
    cos l_{x}\cos b_{x}&\sin l_{z}\cos b_{z}\sin b_{x}-\sin b_{z}\sin l_{x}\cos b_{x}&\cos l_{z}\cos b_{z}\\\sin l_{x}\cos b_{x}&\sin b_{z}\cos l_{x}\cos...
    7 KB (786 words) - 01:41, 24 November 2023
  • Thumbnail for Weierstrass function
    n cos ⁡ ( b n π x ) , {\displaystyle f(x)=\sum _{n=0}^{\infty }a^{n}\cos(b^{n}\pi x),} where 0 < a < 1 {\displaystyle 0<a<1} , b {\displaystyle b} is...
    18 KB (2,287 words) - 09:24, 12 March 2024
  • a\sin b&={\frac {\cos(a-b)-\cos(a+b)}{2}}\\[6pt]\cos a\cos b&={\frac {\cos(a-b)+\cos(a+b)}{2}}\\[6pt]\sin a\cos b&={\frac {\sin(a+b)+\sin(a-b)}{2}}\\[6pt]\cos...
    13 KB (1,913 words) - 22:21, 27 March 2024
  • trigonometric identity cos ⁡ ( a − b ) = cos ⁡ ( a ) cos ⁡ ( b ) + sin ⁡ ( a ) sin ⁡ ( b ) {\displaystyle \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)} , the spherical...
    7 KB (1,157 words) - 17:14, 2 March 2024
  • medium. For instance, such a veto is used in the gamma ray observatory COS-B. Detectors relying on coincidence designs are limited by random, chance...
    14 KB (1,760 words) - 13:29, 21 February 2024
  • Thumbnail for Solar irradiance
    law of cosines: cos⁡(c)=cos⁡(a)cos⁡(b)+sin⁡(a)sin⁡(b)cos⁡(C){\displaystyle \cos(c)=\cos(a)\cos(b)+\sin(a)\sin(b)\cos(C)} where a, b and c are arc lengths...
    56 KB (6,742 words) - 07:09, 14 March 2024