What is taylor cos(x+pi/2) ?

The answer to taylor cos(x+pi/2) is -x+1/6 x^3-1/120 x^5+1/5040 x^7-1/362880 x^9+\ldots

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taylor cos(x+pi/2)

taylor

cos (x + \frac{π}{2})

- x + \frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= - x + \frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

What is taylor cos(x+pi/2) ?
The answer to taylor cos(x+pi/2) is -x+1/6 x^3-1/120 x^5+1/5040 x^7-1/362880 x^9+\ldots