How do you evaluate sin−1(sin(5π3))?

2 Answers
A08
Mar 18, 2016

=5π3

Explanation:

Given sin−1(sin(5π3))
We know that
sin−1(sin(x))=sin−1(sin(x))=(x)
or =x

Following this we obtain
sin−1(sin(5π3))=5π3

Nghi N.
Mar 18, 2016

4π3,5π3

Explanation:

Trig unit circle and trig table give -->
sin(5π3)=sin(−π3+6π3)=sin(−π3+2π)=
=−sin(π3)=−√32.
Next, find arcsin(−√32)
x=−√32 --> 2 solutions -->
arc x=4π3 and arc x=−π3 , or x=5π3 (co-terminal)

Check.
x=4π3 --> sinx=−sinπ3=−√32=sin(5π3). OK
x=5π3 --> sinx=−sin(π3)=−√32=sin(5π3). OK

Related questions
See all questions in Basic Inverse Trigonometric Functions
Impact of this question
12439 views around the world
You can reuse this answer
Creative Commons License