Evaluate : arctan 2 + arctan 3?

Question

Thanks for the tecnology advice..but i appreciate a manual calculation..

Answer 1

Most scientific calculators (even cheap TI-30X for under $10.00) have an inverse tangent function. It is usually above the [TAN] key, and you press [2nd] [TAN] or something like that. It will read: TAN-1 or INV TAN.

This one is easy. Enter 2, then do the inverse tangent function, then do it for 3, and add them together.

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Answer 2

This is a fun one. Try this.

arctan(2)+arctan(3)=x
tan{arctan(2)+arctan(3)}=tan(x)

tan(x+y)=(tan(x)+tan(y))/(1-tan(x)tan(y))

tan(x)=(2+3)/(1-(2)(3))=5/-5=-1

arctan(-1)=3pi/2 or 5pi/2

This takes advantage of the fact arctan(tan(x))=tan(arctan(x))=x

Answer 3

x=arctan2 + arctan3

tanx = (2+3)/(1-6) by tangent addition formula

tanx=-1, which implies x=3pi/4 since arctan2 and arctan3 are in first quadrant

Answer 4

Arctan2