Arctan Formula

In mathematics subject, every function has an inverse. Similarly, the trigonometric function also comprises inverse. In trigonometry, arctan is the inverse of the tangent function and is used to compute the angle measure from the tangent ratio (tan = opposite/adjacent) of a right triangle. Arctan can be calculated in terms of degrees and as well as radians.

arctan(x)=2arctan(x1+1+x2)

arctan(x)=0x1z2+1dz;|x|1

arctan(z)dz=zarctan(z)12ln(1+z2)+C

Arctangent formulas for
π

π4=4arctan15arctan1239

π4=arctan12+arctan13

π4=2arctan12arctan17

π4=2arctan13+arctan17

π4=8arctan1104arctan1515arctan1239

π4=3arctan14+arctan120+arctan11985

π4=24arctan18+8arctan157+4arctan1239

Solved Example

Question : Evaluate: tan-1(1.732)

Solution:

The given value is, tan-1(1.732)

From this given quantity, 1.732 can be written as a function of tan.

So, 1.732 = tan 60°

Therefore, tan-1(1.732) = tan-1 (tan 60°) = 60°

60° = 60

×
 
π180
= 1.047 radians.

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