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Find principal value of the expression \( cos^{-1}(cos(-680^{\circ})).\)

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1 Answer

\(680^{\circ}\) is not in the principal interval of cos which is \([0,180^{\circ}]\)
Therefore reduce the angle within the principal interval using the result
\(cos(n\times\:360^{\circ}-\theta)=cos\theta\)
\( cos^{-1}cos( 720^{\circ}-40^{\circ})=cos^{-1}cos(2\times\:360^{\circ}-40^{\circ})\)
=\( cos^{-1}cos40^{\circ}=40^{\circ}\)

 

answered Feb 28, 2013 by thanvigandhi_1
edited Mar 18, 2013 by rvidyagovindarajan_1
 
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