Math 1700 Worksheet 1: Inverse Trigonometric
Functions and Their Derivatives
1. For the following expressions, simplify the expression if it is well-defined, or
explain why it is not defined.
−1
(a) sin sin
π (b) cos
4
(c) sin−1 cos−1 (−1)
−1
27π
cos
5
(d) sin cot−1
1
2π
csc
2
3
1
−1
(e) cos sin
−
3
3
−1
(f) cot cos
−
5
(g) sin tan−1 (2x)
(h) cos 2 sec−1 (x)
2. Find the domain of the function cos−1
x−1
2
3
+ tan−1
.
x
3. Use implicit differentiation to derive the formula for the derivative of cot−1 (x).
4. Differentiate the following functions. Simplify the answer as much as
possible.
x2
x2 + 1
x
1
(a) y = tan−1
a
a
(b) y = sin−1
(c) y = x · sin cos−1 (x)
(d) y = ln sec−1 (3x)