find the domains of following functions

Question

The domain of arccot(x) is .

The domain of arcsec(x) is .

The range of arccos⁡(x) is .

The range of arcsin⁡(x) is .

Note that you must enter the appropriate intervals here. 

Endpoints of intervals: If an endpoint is included, then use [ or ]. If not, then use ( or ). For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7].

Infinite intervals: For infinite intervals, use Inf for ∞ (infinity) or -Inf for −∞ (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed [6,Inf).

Unions of intervals: If the set includes more than one interval, they are joined using the union symbol U. For example, the set consisting of all points in (-3,7] together with all points in [-8,-5) is expressed [-8,-5)U(-3,7].

Special symbols: You can use R as a shorthand for all real numbers. So, it is equivalent to entering (-Inf, Inf).

Answer 1

Trig. functions have a domain defined everywhere (-Ꝏ,Ꝏ), except for Tan, which is undefined when cos is 0, and Cot, which is undefined when sin is 0. However, they are not 1-1 functions. A 1-1 function is a function that passes the horizontal line test: Only one y-value can correspond to one x value.

Trig functions are made 1-1 by restricting the domains. Once made 1-1, simply swap the domain and range to get the inverse trig functions.