Question

Sin(x)=x- x3/3!+x5/5!-x7/7!+....The percentage relative approximate error in using three terms to find sin(4.1) is ______percent.

Answer 1

The answer is "239.62%".

Explanation:

Given value:

`\bold{\sin(x)=x- (x^3)/(3!)+(x^5)/(5!) - (x^7)/(7!)+....}`

Solve the first three values:

`\sin(x)=x- (x^3)/(3!)+(x^5)/(5!)`

put the value of sin(4.1):

`\to \sin(4.1)=(4.1)- ((4.1)^3)/(3!)+((4.1)^5)/(5!) \\\\`

`=(4.1)- ((4.1)^3)/(3!)+((4.1)^5)/(5!) \\\\=(4.1)- (68.92)/(3 * 2* 1)+(1158.56)/(5* 4 * 3 * 2 * 1)\\\\`

`=(4.1)- 11.48+9.65\\\\= 2.27`

The actual value of
`\sin(4.1) = -1.59`

Calculating the percentage relative approximate error value:

Formula:

`=(actual \ value - \ approx \ value )/(actual \ value) * 100\\\\`

`=(-1.59 - 2.27 )/(-1.59) * 100\\\\= (-3.81)/(-1.59) * 100\\\\= (3.81)/(1.59) * 100\\\\=239.62 \ \%`