Question

If y = sin⁻¹x, −1 ≤ x ≤ 0, then thje range of y is ______.

Options

• `((-pi)/2, 0)`

• `[(-pi)/2, 0]`

• `[(-pi)/2, 0)`

• `((-pi)/2, 0]`

Answer 1

If y = sin⁻¹x, −1 ≤ x ≤ 0, then thje range of y is `bbunderline([(-pi)/2, 0]`.

Explanation:

y = sin⁻¹x, −1 ≤ x ≤ 0

x = sin y

−1 ≤ sin y ≤ 0

`sin(-pi/2) ≤ sin y ≤ sin 0`

`(-pi/2) ≤ y ≤ 0`

Thus, the range of y is `[(-pi)/2, 0]`.