the inverse sine, inverse cosine, and inverse tangent functions have the following domains and ranges…

the inverse sine, inverse cosine, and inverse tangent functions have the following domains and ranges. (enter your answers in interval notation.) (a) the function sin⁻¹ has domain and range. (b) the function cos⁻¹ has domain and range. (c) the function tan⁻¹ has domain and range. resources read it

the inverse sine, inverse cosine, and inverse tangent functions have the following domains and ranges. (enter your answers in interval notation.) (a) the function sin⁻¹ has domain and range. (b) the function cos⁻¹ has domain and range. (c) the function tan⁻¹ has domain and range. resources read it

Answer

Explanation:

Step1: Recall domain - range of inverse sine

The inverse - sine function (y = \sin^{-1}(x)) is defined for values of (x) such that (- 1\leqslant x\leqslant1), and its range is (\left[-\frac{\pi}{2},\frac{\pi}{2}\right]).

Step2: Recall domain - range of inverse cosine

The inverse - cosine function (y=\cos^{-1}(x)) is defined for values of (x) such that (-1\leqslant x\leqslant1), and its range is ([0,\pi]).

Step3: Recall domain - range of inverse tangent

The inverse - tangent function (y = \tan^{-1}(x)) is defined for all real numbers (x), i.e., ((-\infty,\infty)), and its range is (\left(-\frac{\pi}{2},\frac{\pi}{2}\right)).

Answer:

(a) Domain: ([-1,1]), Range: (\left[-\frac{\pi}{2},\frac{\pi}{2}\right]) (b) Domain: ([-1,1]), Range: ([0,\pi]) (c) Domain: ((-\infty,\infty)), Range: (\left(-\frac{\pi}{2},\frac{\pi}{2}\right))