The range of y=arcsinx

Question

the range of y=arcsinx=(-∏/2, ∏/2)

 

TRUE OR FALSE?

 

 

MY ANSWER: FALSE?????????

Answer 1

Arcsinx is the inverse of sinx.

 

y = 1/(sin(x))

 

 

Lets set sin(x) equal to zero to find our domain.  We will then use that domain to determine our range.

 

sin(x) = 0

 

x = 0        x = π      x = 2π

 

Our domain is    (0, π)∪(π, 2π)

 

The range is the set of y values that satisfy the function.

 

In a coordinate system, angles that are in the y-axis are π/2 and 3π/2.  3π/2 can be interpreted as -π/2 when the angle in the coordinate system rotates clockwise.  Notice that these values are in the domain.

 

Therefore, your range is (-π/2 , π/2).