Ffwythiannau trigonometrig

I ddiddwytho ongl A, enwir yr ochrau fel y canlynol:

• Yr hypotenws yw'r ochor gyferbyn ar ongl sgwâr, yn yr achos yma h. Yr hypotenws yw'r ochor sydd ar hyd fwyaf.
• Yr ochor cyferbyn yw'r ochor gyferbyn i'r ongl yr ydym am ei ddarganfod. Yn yr achos yma a.
• Yr ochor cyfagos yw'r ochor sydd rhwng yr ongl yr ydym am ei ddarganfod ar ongl sgwâr. Yn yr achos yma b.

Ffwythiant	Talfyriad	Disgrifiad	Unfathiannau (yn defnyddio radiannau)
Sin	sin	${\displaystyle {\frac {\textrm {cyferbyn}}{\textrm {hypotenws}}}}$	${\displaystyle \sin \theta \equiv \cos \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\csc \theta }}}$
Cosin	cos	${\displaystyle {\frac {\textrm {agos}}{\textrm {hypotenws}}}}$	${\displaystyle \cos \theta \equiv \sin \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\sec \theta }}\,}$
Tangiad	tan (or tg)	${\displaystyle {\frac {\textrm {cyferbyn}}{\textrm {agos}}}}$	${\displaystyle \tan \theta \equiv {\frac {\sin \theta }{\cos \theta }}\equiv \cot \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\cot \theta }}}$
Cotangiad	cot (or ctg or ctn)	${\displaystyle {\frac {\textrm {agos}}{\textrm {cyferbyn}}}}$	${\displaystyle \cot \theta \equiv {\frac {\cos \theta }{\sin \theta }}\equiv \tan \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\tan \theta }}}$
Secant	sec	${\displaystyle {\frac {\textrm {hypotenws}}{\textrm {agos}}}}$	${\displaystyle \sec \theta \equiv \csc \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\cos \theta }}}$
Cosecant	csc (or cosec)	${\displaystyle {\frac {\textrm {hypotenws}}{\textrm {cyferbyn}}}}$	${\displaystyle \csc \theta \equiv \sec \left({\frac {\pi }{2}}-\theta \right)\equiv {\frac {1}{\sin \theta }}}$

Mae yna nifer o unfathiannau yn bodoli sy'n cydberthyn y ffwythiannau trigonometrig. Dyma'r un a defnyddir fwya' aml.

${\displaystyle \sin ^{2}x+\cos ^{2}x=1,\,}$

Perthnasau arall sy'n bodoli yw'r fformiwlâu swm a gwahaniaeth.

${\displaystyle \sin \left(x+y\right)=\sin x\cos y+\cos x\sin y,\,}$

${\displaystyle \cos \left(x+y\right)=\cos x\cos y-\sin x\sin y,\,}$

${\displaystyle \sin \left(x-y\right)=\sin x\cos y-\cos x\sin y,\,}$

${\displaystyle \cos \left(x-y\right)=\cos x\cos y+\sin x\sin y.\,}$

Pan mae dwy ongl yn hafal, mae'r swm y fformiwlâu yn symleiddio i hafaliadau a adnabyddir fel y double-angle formulae.

Calcwlws

Mae'r tabl yma yn dangos integriadau a differiadau ffwythiannau trigonometreg.

Ffwythiant ${\displaystyle \ \ \ \ f(x)}$	Differu ${\displaystyle \ \ \ \ f'(x)}$	Integru ${\displaystyle \int f(x)\,dx}$
${\displaystyle \,\ \sin x}$	${\displaystyle \,\ \cos x}$	${\displaystyle \,\ -\cos x+C}$
${\displaystyle \,\ \cos x}$	${\displaystyle \,\ -\sin x}$	${\displaystyle \,\ \sin x+C}$
${\displaystyle \,\ \tan x}$	${\displaystyle \,\ \sec ^{2}x=1+\tan ^{2}x}$	${\displaystyle -\ln \left|\cos x\right|+C}$
${\displaystyle \,\ \cot x}$	${\displaystyle \,\ -\csc ^{2}x=-(1+\cot ^{2}x)}$	${\displaystyle \ln \left|\sin x\right|+C}$
${\displaystyle \,\ \sec x}$	${\displaystyle \,\ \sec {x}\tan {x}}$	${\displaystyle \ln \left|\sec x+\tan x\right|+C}$
${\displaystyle \,\ \csc x}$	${\displaystyle \,\ -\csc {x}\cot {x}}$	${\displaystyle \ -\ln \left|\csc x+\cot x\right|+C}$