स्पर्शिका उलट कार्य, कोनांना दिलेल्या संख्येइतकी स्पर्शिका असते,

arctan's Usage Examples:

"On Irrationality Measure of arctan 1/3".

formulae are used in conjunction with the Taylor series expansion for arctangent: The following equations were derived in Angle addition formula: sin ⁡.

( x ; 0 , 1 ) 1 2 + 1 π arctan ⁡ ( ln ⁡ x ) ,     x > 0 {\displaystyle F(x;0,1){\frac {1}{2}}+{\frac {1}{\pi }}\arctan(\ln x),\ \ x>0} The survival.

horizontally, α h 2 arctan ⁡ h 2 f 2 arctan ⁡ 36 2 × 50 ≈ 39.

{\displaystyle \operatorname {atan2} (y,x)} or arctan2 ⁡ ( y , x ) {\displaystyle \operatorname {arctan2} (y,x)} (from "2-argument arctangent") is defined.

The graph of the derivative of the arctangent function forms an example of the witch of Agnesi.

{\displaystyle x\arcsin(\cos \varphi \sin \lambda )\qquad y\arctan \left({\frac {\tan \varphi.

known as Gregory"s series, can be given by: arctan ⁡ x x − x 3 3 + x 5 5 − x 7 7 + ⋯ {\displaystyle \arctan xx-{\frac {x^{3}}{3}}+{\frac {x^{5}}{5}}-{\frac.

θ arctan ⁡ x {\displaystyle \theta \arctan x} .

4 2 arctan ⁡ 1 3 + arctan ⁡ 1 7 {\displaystyle {\frac {\pi }{4}}2\arctan {\frac {1}{3}}+\arctan {\frac {1}{7}}} π 4 4 arctan ⁡ 1 5 − arctan ⁡ 1 239.

Machin's original formula,\textstyle\pi 16\arctan \frac15 - 4\arctan\frac1{239},is of this type, and Størmer showed that there were three other ways of representing as a rational combination of two Gregory numbers.

where arctan is the inverse (circular) tangent function.