Chapter 6.5, Problem 1E

CONCEPTS

(a) To define the inverse sine function, we restrict the domain of sine to the interval ______. On this interval the sine function is one-to-one, and its inverse function ${\sin }^{-1}$ is defined by ${\sin }^{-1}x=y\iff \sin \_\_\_\_\_\_$=______. For example, ${\sin }^{-1}\frac{1}{2}=\_\_\_\_\_\_$ because sin ______ = _______.

(b) To define the inverse cosine function, we restrict the domain of cosine to the interval __________. On this interval the cosine function is one-to-one, and its inverse function ${\cos }^{-1}$ is defined by ${\cos }^{-1}x=y\iff \cos \_\_\_\_\_=\_\_\_\_\_$. For example, ${\cos }^{-1}\frac{1}{2}=\_\_\_\_\_\_$ because cos _______ = ________.