Derivative Problem

[Euler]

I was doing a review section in my calculus book, and I am not getting the answer that it says I should be getting.

The book wants me to find the average rates of change when t=3.9 to t=4 and t=4 to t=4.1, and then calculate the instantaneous rate t=4.

The equation is: d=90-80sin(1.2)(t-3)

Now, the book says the average rates of change are DIFFERENT for t=3.9 to t=4 and t=4 to t=4.1. When I plug in the numbers, I find that they are the same (~-7.45) Obviously my instantaneous rate is going to be off due to the fact that my average rates are coming out wrong.

What am I missing? Even when I divide by my time interval the answer is still way off.

 

[Gene]

You don't say what answer the book gives nor do you show the what you are doing. I get a completly different answer.
Average rate of change is
f(y₂)-f(y₁)/(x₂-x₁)
Be sure your calculator (book, sliderule, abacus?) is set to radians.
The instanious rate of change would ususlly be d(d)/d(t), a different equation.