We Know that For a function to have an inverse function, it must be one-to-one—that
is, it must pass the Horizontal Line Test.
1. On the interval [–pi/2, pi/2], the function
y = sin x is
increasing 2. On the interval [–pi/2, pi/2], y = sin x takes on its full
range of values, [–1, 1] 3. On the interval [–pi/2, pi/2], y = sin x is
one-to-one sin x has an inverse function
on this interval [–pi/2, pi/2]
On the restricted domain [–pi/2, pi/2] y = sin x has a
unique inverse function called the inverse sine function. <span>f(x) = sin−1(x) </span>the range of y=sin x in the domain [–pi/2, pi/2] is [-1,1] the range of y=sin-1 x in the domain [-1,1] is [–pi/2, pi/2]
1. On the interval [0, pi], the function y = cos x is decreasing 2. On the interval [0, pi], y = cos x takes on its full range of values, [–1, 1] 3. On the interval [0, pi], y = cos x is one-to-one cos x has an inverse function on this interval [0, pi]
On the restricted domain [0, pi] y = cos x has a unique inverse function called the inverse sine function. f(x) = cos−1(x) the range of y=cos x in the domain [0, pi] is [-1,1] the range of y=cos-1 x in the domain [-1,1] is [0, pi]
the answer is
<span>the values of the range are different because the domain in which the inverse function exists are different</span>
