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Activity 2.4.3.
Let
\(p(x) = \csc(x)\) and recall that
\(\csc(x) = \frac{1}{\sin(x)}\text{.}\)
(a)
What is the domain of
\(p\text{?}\)
(b)
Use the quotient rule to develop a formula for
\(p'(x)\) that is expressed completely in terms of
\(\sin(x)\) and
\(\cos(x)\text{.}\)
(c)
How can you use other relationships among trigonometric functions to write
\(p'(x)\) only in terms of
\(\cot(x)\) and
\(\csc(x)\text{?}\)
(d)
What is the domain of
\(p'\text{?}\) How does this compare to the domain of
\(p\text{?}\)
