Help on Linear Approximation

[tuansmart]

Estimate ?f using the Linear Approximation and use a calculator to compute both the error and the percentage error.
f(x)=cos(x), a=(?/4), ?x=0.04
This is an online homework.
I got ?f=-.02828, error is .00056, and the percentage error is 1.94%. My ?f is correct, but my error and percentage error is incorrect. I did this three times, and I got the same errors. Can somebody help me?

 

[Deleted member 4993]

Estimate ?f using the Linear Approximation and use a calculator to compute both the error and the percentage error.
f(x)=cos(x), a=(?/4), ?x=0.04
This is an online homework.
I got ?f=-.02828, error is .00056, and the percentage error is 1.94%. My ?f is correct, but my error and percentage error is incorrect. I did this three times, and I got the same errors. Can somebody help me?

Please show your work.

That'll tell us where to begin to help you.

 

[tuansmart]

Estimate ?f using the Linear Approximation and use a calculator to compute both the error and the percentage error.
f(x)=cos(x), a=(?/4), ?x=0.04
f(x)'=-sin(x), ?f=f(a)'?x
=-sin(?/4)0.04=-.02828
Actual change: ?f=f(a+?x)-f(a)
=cos(?/4+.04)-cos(?/4)=-.02884
Error: |-.02884-(-.02828)|=.00056
Percentage error: .|.00056/-.02884|x100=1.94%