Inverse Trigonometric Functions

Sol A a) (since ).

b) is undefined, since 5/3 is not in .

Sol B a) (since for any ).

b) , so since the tangent has period , and is in ; so .

Sol 1 a) , since and .

b) , since and .

Sol 2 a) , since and .

b) , since and .

Sol 3 a) since and .

b) since and .

Sol 4 Let , so From the right triangle shown below, ; so .

Sol 5 Let , so . From the right triangle shown below, ; so .

Sol 6 Let , so . Then .

Sol 7 Let , so . Then and using the right triangle below, so .

Sol 8 Since , where ; so .

Lawrence Marx 2002-07-12