<Dd> sin ⁡ (x + 2 π) = sin ⁡ (x) (\ displaystyle \ sin (x + 2 \ pi) = \ sin (x)) </Dd> <P> for every real x (and more generally sin (x + 2πn) = sin (x) for every integer n). However, the sine is one - to - one on the interval (− π / 2, π / 2), and the corresponding partial inverse is called the arcsine . This is considered the principal branch of the inverse sine, so the principal value of the inverse sine is always between − π / 2 and π / 2 . The following table describes the principal branch of each inverse trigonometric function: </P> <Dl> <Dd> <Table> <Tr> <Th> function </Th> <Th> Range of usual principal value </Th> </Tr> <Tr> <Td> arcsin </Td> <Td> − π / 2 ≤ sin (x) ≤ π / 2 </Td> </Tr> <Tr> <Td> arccos </Td> <Td> 0 ≤ cos (x) ≤ π </Td> </Tr> <Tr> <Td> arctan </Td> <Td> − π / 2 <tan (x) <π / 2 </Td> </Tr> <Tr> <Td> arccot </Td> <Td> 0 <cot (x) <π </Td> </Tr> <Tr> <Td> arcsec </Td> <Td> 0 ≤ sec (x) ≤ π </Td> </Tr> <Tr> <Td> arccsc </Td> <Td> − π / 2 ≤ csc (x) ≤ π / 2 </Td> </Tr> </Table> </Dd> </Dl> <Dd> <Table> <Tr> <Th> function </Th> <Th> Range of usual principal value </Th> </Tr> <Tr> <Td> arcsin </Td> <Td> − π / 2 ≤ sin (x) ≤ π / 2 </Td> </Tr> <Tr> <Td> arccos </Td> <Td> 0 ≤ cos (x) ≤ π </Td> </Tr> <Tr> <Td> arctan </Td> <Td> − π / 2 <tan (x) <π / 2 </Td> </Tr> <Tr> <Td> arccot </Td> <Td> 0 <cot (x) <π </Td> </Tr> <Tr> <Td> arcsec </Td> <Td> 0 ≤ sec (x) ≤ π </Td> </Tr> <Tr> <Td> arccsc </Td> <Td> − π / 2 ≤ csc (x) ≤ π / 2 </Td> </Tr> </Table> </Dd>

If the function f(x) = mx + b has an inverse function