The Maclaurin series for sin−1(x) is given by sin−1(x) = x + [infinity] n = 1 1 · 3 · 5 (2n − 1) 2 · 4 · 6 (2n) x2n+1 2n + 1 . Use the first five terms of the Maclaurin series above to approximate sin−1 3 7 . (Round your answer to eight decimal places.)

0.44290869

Step-by-step explanation:

The Maclaurin series for sin⁻¹(x) is given by

sin⁻¹(x) = x +

Use the first five terms of the Maclaurin series above to approximate sin⁻¹ . (Round your answer to eight decimal places.)

Answer

sin⁻¹(x) = x +

in the above equation  summation from n=1 to ∞

we are estimating this for the first 5 terms as follows

sin⁻¹(x) = x +    +    +    +  

sin⁻¹(x) = x +    +    +  +    

now to get

sin⁻¹() substitute

hence,

sin⁻¹() =  

sin⁻¹() = 0.42857142 + 0.01311953 + 0.00108437 + 0.00011855 + 0.00001482

           =  0.44290869

could

step-by-step explanation:

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x = 3 ± √(5+y)