MATH 100 V1A
October 10th – Practice problems
1. (a) Sketch the graph of sin x1 . Is this function continuous? (You may assume that
trigonometric functions are continuous on their domain; see Spiderwire for a proof.)
(b) Is the function
(
sin
f (x) =
0
1
x
if x 6= 0
if x = 0
continuous?
2. In class, we claimed
that the function g(x) = ax3 + bx2 + 1, where a =
b = π1 π3 − 2 , makes the function


if x < 0
tan(x)
f (x) = g(x)
if 0 ≤ x ≤ π


cos(sin(x)) if x > π
differentiable for all x > − π4 . Prove that this is true.
3. Sketch and find the equation of the line tangent to y = sin x at x = π.
4. Find the equation of the line tangent to y = cos2 (x) at x = π3 .
5. Explain why sin
π
6
= sin − 11π
.
6
6. Sketch the graphs of csc(θ) =
1
,
sin(θ)
sec(θ) =
1
cos(θ)
and cot(θ) =
1
.
tan(θ)
1
π2
1−
2
π
and