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2.4. DERIVATIVES OF OTHER TRIGONOMETRIC FUNCTIONS
(b) True or false: for all real numbers x, f (x) = cos(x).
(c) Explain why the function that you found in (a) is almost the opposite of the
sine function, but not quite. (Hint: convert all of the trigonometric functions
in (a) to sines and cosines, and work to simplify. Think carefully about the
domain of f and the domain of f ′ .)
3. Let p(z) be given by the rule
p(z) =
z tan(z)
z 2 sec(z) + 1
+ 3e
z + 1.
(a) Determine p ′ (z).
(b) Find an equation for the tangent line to p at the point where z = 0.
(c) At z = 0, is p increasing, decreasing, or neither? Why?
2.4. DERIVATIVES OF OTHER TRIGONOMETRIC FUNCTIONS
(b) True or false: for all real numbers x, f (x) = cos(x).
(c) Explain why the function that you found in (a) is almost the opposite of the
sine function, but not quite. (Hint: convert all of the trigonometric functions
in (a) to sines and cosines, and work to simplify. Think carefully about the
domain of f and the domain of f ′ .)
3. Let p(z) be given by the rule
p(z) =
z tan(z)
z 2 sec(z) + 1
+ 3e
z + 1.
(a) Determine p ′ (z).
(b) Find an equation for the tangent line to p at the point where z = 0.
(c) At z = 0, is p increasing, decreasing, or neither? Why?