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

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