Question

How do you find the exact value of sin(arctan(2))?

Answer 1

Let `alpha` = arctan(2), then, we require the value of sin`alpha` . now tan `alpha` = 2`=>` sin`alpha` = 2/`sqrt`5.

Explanation:

tan`alpha` = 2 `=>` y= 2a, x = 2a & r = `sqrt` (5`a^2` ) = `sqrt5` a
sin`alpha` = 2a/ `sqrt5` a = 2/`sqrt5`