Please help! Algebra 2!!

Question

1.) What is the inverse of y = sin x? Give the equation.

Answer 1

the domain of f(x)=sinx is (-infinity,+infinity), the range is [-1,1]

the domain of sin^-1x is [-1,+1], and for sin^-1x to be a function the range is limited to (-π/2,+-π/2]

if the value of x in sin^-1x is 1/2, then y=sin^-1x has multiple values, [π/6+2kπ], and [2m+1)π-π/6]

where k and m are 0,+/-1,+/-2,...

k=0 and m=0 give "principal value" returned in calculator)=π/6 for x=1/2 and viable 5π/6 for third quadrant result.

Answer 2

The inverse of the sine function is the arcsine, or sin^-1.

y = arcsin x

y = sin^-1 x