Hey puresoul.

For d) I got

99-100=10cos(500t) which means

-1/10 = cos(500t) which means

> acos(-1/10)

[1] 1.670964 implies that

500t = 1.670964 (approx) which means t is given by

> acos(-1/10)/500

[1] 0.003341927

Checking the answer gives us:

> x = acos(-1/10)/500

> 100 + 10*cos(500*x)

[1] 99

which is correct.

Now you try and obtain the next value of t where this is equal and get the length of the appropriate interval.