How do you solve and find the value of #sin^-1(tan(pi/4))#?

1 Answer
Feb 14, 2017

Answer:

#sin^(-1)(tan(pi/4))=color(green)(pi/2+k * 2pi,AAk in ZZ)#

Explanation:

The angle #pi/4# is one of the standard angles with
#color(white)("XXX")tan(pi/4)=1#

So #sin^(-1)(tan(pi/4))=sin^(-1)(1)#

If we restrict #theta# to the range #[0,2pi)#
the only value of #theta# for which #sin(theta)=1# is #theta=pi/2#

For the unrestricted case, this value will repeat with every complete rotational cycle,
so #theta=pi/2+k * 2pi, AAkinZZ#