How do you find arcsin(-1/2) ?

2 Answers
Jun 22, 2018

#arc sin(-1/2)=-pi/6#

Explanation:

We know that,

#color(red)((1)arc sin(-x)=-arc sinx#

#color(blue)((2)arc sin(sintheta)=theta ,theta in[-pi/2,pi/2]#

Now,

#arc sin(-1/2)=-arc sin(1/2)...tocolor(red)([Apply(1)]#

#arc sin(-1/2)=-arc sin(sin(pi/6))to[because sin(pi/6)=1/2]#

#arc sin(-1/2)=-pi/6...tocolor(blue)(Apply(2)#

Jun 23, 2018

arc #x = (7pi)/6#
arc #x = (11pi)/6#

Explanation:

sin x = - 1/2
Trig table and unit circle give 2 arcs x that have the same sin value (-1/2):
#x = - pi/6#, or #x = (11pi)/6# (co-terminal), and
#x = pi - (-pi/6) = (7pi)/6#