Question

Find the principal of$\sf \: cos ^{ - 1} \bigg[ - \dfrac{1}{2} \: \: \bigg ]$


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Answer 1

Answer:

Cos ( 2π/3 )

Step-by-step explanation:

Range = ( 0, 180 ) = ( 0, π )

We know that Cos function is negative only in 2 quadrant in its range.

Hence, let us assume A = Cos⁻¹ ( -1/2 )

⇒ Cos A = -1/2

We know that, Cos 60 is only 1/2 in first quadrant. Hence in second quadrant it would be ( 180 - 60 ), which is 120°

120 is 2π/3.

Hence Principal Value of Cos⁻¹ ( -1/2 ) is ( 2π/3 ).

Answer 2

Go through the Attachment

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