which trigonometric functions have a domain of -1, 1?\n y = arcsinx and y = arccosx\n y = arccosx and y =…

Answer:

A. ( y = \arcsin x ) and ( y = \arccos x )

Explanation:

Step1: Recall domain of inverse trigonometric functions

• For ( y=\arcsin x ), by definition, ( - 1\leqslant x\leqslant1 ).
• For ( y = \arccos x ), by definition, ( - 1\leqslant x\leqslant1 ).

Step2: Check other functions

• For ( y=\arctan x ), the domain is ( (-\infty,\infty) ) since ( y = \tan x) (original function) has a range of ( (-\infty,\infty) ) and we take the inverse.
• For ( y=\text{arcsec}x), ( y=\text{arcsec}x=\arccos\left(\frac{1}{x}\right)), domain is ( (-\infty,- 1]\cup[1,\infty) ).
• For ( y=\text{arccsc}x), ( y=\text{arccsc}x=\arcsin\left(\frac{1}{x}\right)), domain is ( (-\infty,- 1]\cup[1,\infty) ).