Inverse Trigonometric Functions

Question 1

y=arcsin(x) if and only if

Answer 1

sin(y)=x and y∈[-Π/2 , Π/2]

Question 2

y=arccos(x) if and only if

Answer 2

cos(y)=x and y∈[0 , Π]

Question 3

y=arctan(x) if and only if

Answer 3

tan(y)=x and y∈(-Π/2 , Π/2)

Question 4

y=arccot(x) if and only if

Answer 4

cot(y)=x and y∈(0 , Π)

Question 5

y=arcsec(x) if and only if

Answer 5

sec(y)=x and y∈[0 , Π] but y≠Π/2

Question 6

y=arccsc(x) if and only if

Answer 6

csc(y)=x and y∈[-Π/2 , Π/2] but y≠0