http://www.ck12.org Chapter 5. Trigonometric Functions
cot(csc−^1 (−^135 ))=−^125
Concept Problem Revisited
Since arcsine only produces angles between−π 2 andπ 2 or− 90 ◦to+ 90 ◦the result of sin−^1 (sin 370◦)is 10◦which is
coterminal to 370◦.
Vocabulary
Restricted domainrefers to the fact that when creating an inverse you sometimes must cut off the domain of most
of the function, saving the largest possible portion so that when the inverse is created it is also a function.
Guided Practice
- What is the graph ofy=tan−^1 x?
- What is the graph ofy=csc−^1 x?
- Evaluate the expression csc(cot−^1 [−^86 ]).
Answers: - Graph the portion of tangent that fits the horizontal line test and reflect across the liney=x. Note that the graph
of arctan is in blue. - Graph the portion of cosecant that fits the horizontal line test and reflect across the liney=x.