Question

Find the value of sin^-1 (sin3π/5) ​

Answer 1

Step-by-step explanation:

The value of sin^(-1) ( sin 3π/5 ) is supposed to be equal to 3π/5 

But actually it's not! 

For sin^(-1) ( sin x ) , x must be within [-π/2, π/2] 

Clearly 3π/5 > π/2 

So, 

sin^(-1) ( sin 3π/5 ) = sin^(-1) ( sin (π - 3π/5 )) = sin^(-1) ( sin 2π/5 ) = 2π/5 ∈ [-π/2, π/2] 

The answer is 2π/5

Answer 2

Answer:

2π/5

Step-by-step explanation:

We know that sin^-1(sinx) = x

therefore, sin-¹sin(3π/5)= 3π/5

but , it doesn't lie in [-π/2, π/2 ]

Since, sin(3π/5) = sin ( π-3π/5) = sin(2π/5)

which lie in [-π/2,π/2]

Therefore , sin^-1sin(2π/5) = 2π/5 Answer .

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Hope it's helpful !

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