How do you find the exact value of #arcsin(sin((7pi)/3))#?

1 Answer
Jul 23, 2015

#arcsin(sin((7pi)/3)) = pi/3#

Explanation:

As an argument to a trigonometric function:
#color(white)("XXXX")##(7pi)/3# is equivalent to #pi/3#
#color(white)("XXXX")##color(white)("XXXX")#(since #(7pi)/3 = 2pi+pi/3#)

Provided #theta# is within #[0, pi]#
#color(white)("XXXX")##arcsin(sin(theta)) = theta#
#color(white)("XXXX")##color(white)("XXXX")#(basic definition)

So
#arcsin(sin((7pi)/3))#
#color(white)("XXXX")##= arcsin(sin(pi/3))#
#color(white)("XXXX")##= pi/3#