The question: Find the value of cos(pi/5) using the Taylor series approximation to sigma(pi/5)^4.

My solution: cos(pi/5)=1- ((pi^2)/50) + sigma(pi/5)^4
cos(pi/5)=0.8026079 + sigma(pi/5)^4

cos(pi/5)=0.8090170 and to find actual error
sigma(pi/5)^4 = 0.8090170-0.8026079=0.0064090

the only problem is that it doesn't satisfy the condition that:

|d^3(cosx)/dt^3|max * ((pi/5)^4)/4! =0.0052537

which is smaller than actual error in magnitude. According to the rule,it should be opposite. So where am i doing wrong? Thanks.

Question

The question: Find the value of cos(pi/5) using the Taylor series approximation to sigma(pi/5)^4.

My solution: cos(pi/5)=1- ((pi^2)/50) + sigma(pi/5)^4
cos(pi/5)=0.8026079 + sigma(pi/5)^4

cos(pi/5)=0.8090170 and to find actual error>>>
sigma(pi/5)^4 = 0.8090170-0.8026079=0.0064090

the only problem is that it doesn't satisfy the condition that:

|d^3(cosx)/dt^3|max  * ((pi/5)^4)/4! =0.0052537

which is smaller than actual error in magnitude. According to the rule,it should be opposite. So where am i doing wrong? Thanks.