What is maclaurin sin(pi/6+x) ?

The answer to maclaurin sin(pi/6+x) is 1/2+(sqrt(3))/2 x-1/4 x^2-1/(4sqrt(3))x^3+1/48 x^4+\ldots

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maclaurin sin(pi/6+x)

maclaurin

sin (\frac{π}{6} + x)

\frac{1}{2} + \frac{3}{2} x - \frac{1}{4} x^{2} - \frac{1}{4 3} x^{3} + \frac{1}{48} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= \frac{1}{2} + \frac{\frac{d}{d x} ( sin ( \frac{π}{6} + x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( \frac{π}{6} + x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( \frac{π}{6} + x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{2} + \frac{\frac{3}{2}}{1 !} x + \frac{- \frac{1}{2}}{2 !} x^{2} + \frac{- \frac{3}{2}}{3 !} x^{3} + \frac{\frac{1}{2}}{4 !} x^{4} + \dots

Refine

= \frac{1}{2} + \frac{3}{2} x - \frac{1}{4} x^{2} - \frac{1}{4 3} x^{3} + \frac{1}{48} x^{4} + \dots

\frac{d}{d x} (1 - e^{- 4 x})

\int 1^{\frac{1}{2}}

\frac{- x ^{2} - 4 x}{( x ^{2} - x - 2 ) ^{2}}

n = 1 \sum \infty 4 \cdot 0. 3^{n}

\frac{\partial}{\partial x} (x^{7} y z^{2} + 7 yz)

What is maclaurin sin(pi/6+x) ?
The answer to maclaurin sin(pi/6+x) is 1/2+(sqrt(3))/2 x-1/4 x^2-1/(4sqrt(3))x^3+1/48 x^4+\ldots