What is the value of #cos^-1(cos(-pi/3))#?

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Answer 1 · 2016-07-23T17:35:08

#cos^-1(cos(-pi/3))=pi/3#..

We have, #costheta=cos(-theta), AA theta in RR.............(1)#.

Next let us recall the following defn. of the #cos^-1# function :-

#cos^-1x=theta, |x|<= 1 iff costheta=x, theta in [0,pi]...............(2)#

Now, using #(2)# in #larr# direction, keeping in mind that #costheta <=1# ,

we have, #cos^-1(costheta)=theta, if, theta in [0,pi]...................(2')#

Now, #cos^-1(cos(-pi/3))=cos^-1(cos(pi/3))................[by (1)#],

&, here, since #pi/3 in [0,pi]#, we get, by #(2')#,

#cos^-1(cos(-pi/3))=cos^-1(cos(pi/3))=pi/3#..