What is Cos^(-1) [cos(-5pi/3)]?

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1 Answer
Antoine
Sep 21, 2015

#cos^-1[cos((-5pi)/3)]=pi/3#

Explanation:

First get the value of #cos((-5pi)/3)#

For this we need to find the acute angle associated with #(-5pi)/3#

Since #cosx# is of period #2pi#,
the angle #(-5pi)/3# is equivalent to #(2pi+(-5pi)/3)=color(red)(pi/3)#

Hence, #cos^-1[cos((-5pi)/3)]# is the same as #color(green)(cos^-1[cos(pi/3)])#

#cos(pi/3)# is #1/2#

So, #cos^-1[cos(pi/3)]=cos^-1(1/2)#

The function #cos^-1(a)# is just asking us to give the angle whose cosine is #a#

Similarly, #cos^-1(1/2)=color(blue)(pi/3#

In other words, #cos^-1(1/2)# verbally means: "the (acute) angle whose cosine is #1/2#

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