How do you evaluate #arctan 133.3#?

1 Answer
Oct 23, 2017

#arctan(133.3) ~~ 1.56329459205#

Explanation:

Note that:

#arctan x = x - x^3/3+x^5/5-x^7/7+...#

This is practical to use for small values of #x#, but what about #133.3#?

The trick is that:

#arctan(x) = pi/2 - arctan (1/x)#

So we can evaluate #arctan(1/133.3)# and subtract it from #pi/2#.

#arctan (1/133.3) = arctan (10/1333)#

#color(white)(arctan (1/133.3)) ~~ 10/1333 - 10^3/(1333^3*3)#

#color(white)(arctan (1/133.3)) ~~ 10/1333 - 1000/7105779111#

#color(white)(arctan (1/133.3)) ~~ 0.00750173474#

So

#arctan(133.3) ~~ pi/2 - 0.00750173474 ~~ 1.56329459205#