Question

Find the value of sin-¹(sin 2π/3)

Answer 1

Sin2pi/3 can be written as pi-pi/3

As pi-pi/3 comes in second quadrant it will be positive as it is the home of Sinx

The above eqn. Will become

sin inverse(sin pi/3) which will be then equal to the pi/3 as sin inverse(sinx) is x in it principal values which is from [-pi/2,pi/2]

Answer 2

Answer:

π / 3

Step-by-step explanation:

sin-¹(sin 2π/3)

arcsin(sin 2π/3)

By identity sin x = cos (π/2 - x )

arcsin(cos ( π/ 2 - 2π/3))

arcsin(cos ((3π - 4π)/6))

arcsin(cos ((3π - 4π)/6))

arcsin(cos (π/6))

arcsin(1/2)

π / 3