Question

Evaluate cos −1(−1/√2)

Answer 1

Answer:

$\frac{3\pi }{4}$

Step-by-step explanation:

$cos^{-1}(\frac{-1}{\sqrt{2} } )=cos^{-1}(-cos\frac{\pi }{4} )=cos^{-1}(cos(\pi- \frac{\pi }{4} ))=cos^{-1}(cos \frac{3\pi }{4} )=\frac{3\pi }{4}$

Answer 2

cos− 1 (− 1/ 2 ) = 2 π /3

Explanation:

cos ( π/ 3 ) = 1 /2 ,  cos ( π -π /3 ) = − 1 /2

Let cos − 1 ( − 1 /2 ) = θ  ∴ cos θ = ( − 1 /2 )

cos ( 2 π /3 ) = − 1 /2  ∴ cos θ =cos ( 2 π /3 )  ∴ θ = 2 π /3

Hence  cos − 1 ( − 1 /2 ) = 2 π /3

Range of  cos − 1 ( x )  is  [ 0,π ] and 2 π/ 3  is in the range.

So  cos − 1 ( − 1/ 2 ) = 2 π/ 3