How do you simplify #cos^-1 [sin (-pi/4) ]#?

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Answer 1 · 2016-07-11T02:13:57

Use #cos (cos^(-1)a)=a#.

With the principal values as the angles,

#cos ((3pi)/4)=sin (-pi/4)=-1/sqrt 2#

Now, the given expression = #cos^(-1)(cos ((3pi)/4))= (3pi)/4#.

Of course, the general value is

#a=2npi+-(3pi)/4, n=0, +-1, +-2, +-3, ...#.

This sorting comes from

#cos^(-1)cos#(general value); by choice.