What does #arcsin(cos ((5pi)/6)) # equal?

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2 Answers
P dilip_k
Mar 13, 2016

#=-pi/3#

Explanation:

"principal value" of the arcsin function means it's between
#-pi/2<=theta<=+pi/2#

#arcsin(cos(5pi/6))=arcsin(cos(pi/2+pi/3))=arcsin(-sin(pi/3))=arcsinsin(-pi/3)=-pi/3#

for least positve value
#arcsin(cos(5pi/6))=arcsin(cos(pi/2+pi/3))=arcsin(-sin(pi/3))=arcsinsin(pi+pi/3)=4pi/3#

Nghi N.
Mar 18, 2016

#(4pi)/3, (5pi)/3 #

Explanation:

Trig table gives -->
#cos ((5pi)/6) = - sqrt3/2#
Find #arcsin(-sqrt3/2)#
Trig unit circle, and trig table give -->
#sin x = -sqrt3/2# -->2 solutions -->
arc #x = - pi/3# and arc # x = (4pi)/3#
Answers: #((4pi)/3)# and #((5pi)/3) #--> (co-terminal with #(-pi/3)#

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