If the range of the y=sinx and y=cosx is [-1,1] which trigonometric functions have a domain of [-1,1]?

Question

a. y=arcsinx and y=arccosx

b. y=arccosx and y=arctanx

c. y=arcsinx and y=arctanx

d. y=arcsecx and y= arccscx

Answer 1

the sines and cosines of any angle is always between -1 and 1

the inverse functions are arcsinx and arccosx

inverses switch x and y coordinates

if (x,y) is a point on one function, (y,x) is a point on the inverse function

if the range of sinx and cosx is -1 to 1

then the domain of arcsinx and arccosx is -1 to 1

switching x and y is the same as switching range and domain

a is correct

Answer 2

a), since arcsin is the inverse of sin, arccos is the inverse of cos, and sin and cos have a range of [-1, 1].