Question

Find the value of sin⁻¹ (sin $\frac{33\pi}{7}$).

Answer 1

Answer:

The answer to this question is  " 33π/7 "

Step-by-step explanation:

The question is very simple.

sin is a Trigonometric function.

While sin⁻¹ is an Inverse Trigonometric Function of the sin function.

We have given that  

sin⁻¹(sin 33π/7)

Both the functions will cancel each other and we get the answer which is

 " 33π/7 "

Hope that it will help you.

Answer 2

Answer:

sin⁻¹ (sin 33π/7)=2π/7

Step-by-step explanation:

To find the value of

$sin^{-1}(sin\:\frac{33\pi }{7})$

since sin⁻¹ cancels sine function only if 33π/7 lies between principal value branch[-π/2,π/2]

sin(33π/7)=sin(4π-5π/7)

=> sin(5π/7)         ∵periodicity of sine function is 2π

=> sin⁻¹[sin(5π/7)]   here 5π/7 does not lies between[-π/2,π/2]

so,need to convert 5π/7 so that it lies between principal value branch

i.e.[-π/2,π/2]

=> sin(5π/7)=sin(π-2π/7)

since sin(π-θ)=sinθ

so

=> sin(π-2π/7)=sin (2π/7)

now

sin⁻¹ (sin 2π/7)=2π/7    ,-π/2 < 2π/7 < π/2

hope it helps you.