What is maclaurin sin^2(x) ?

The answer to maclaurin sin^2(x) is x^2-1/3 x^4+2/45 x^6-1/315 x^8+2/14175 x^{10}+\ldots

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maclaurin sin^2(x)

maclaurin

sin^{2} (x)

x^{2} - \frac{1}{3} x^{4} + \frac{2}{45} x^{6} - \frac{1}{315} x^{8} + \frac{2}{14175} x^{10} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( sin ^{2} ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ^{2} ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ^{2} ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 8}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{32}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 128}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{512}{10 !} x^{10} + \dots

Refine

= x^{2} - \frac{1}{3} x^{4} + \frac{2}{45} x^{6} - \frac{1}{315} x^{8} + \frac{2}{14175} x^{10} + \dots

\frac{d}{d t} (3 cos (t))

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\int sin^{3} (t) cos^{8} (t) d t

\int_{0}^{\frac{π}{3}} sin (3 t) d t

\int \frac{5}{x ^{2} - 5} d x

What is maclaurin sin^2(x) ?
The answer to maclaurin sin^2(x) is x^2-1/3 x^4+2/45 x^6-1/315 x^8+2/14175 x^{10}+\ldots