What is taylor sin(pi/2-x) ?

The answer to taylor sin(pi/2-x) is 1-1/2 x^2+1/24 x^4-1/720 x^6+1/40320 x^8+\ldots

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taylor sin(pi/2-x)

taylor

sin (\frac{π}{2} - x)

1 - \frac{1}{2} x^{2} + \frac{1}{24} x^{4} - \frac{1}{720} x^{6} + \frac{1}{40320} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 - \frac{1}{2} x^{2} + \frac{1}{24} x^{4} - \frac{1}{720} x^{6} + \frac{1}{40320} x^{8} + \dots

x \to - 1 - lim (x^{2})

x \to 3 - lim (\frac{x ^{2}}{x - 3})

\int 6 x^{\frac{2}{3}} d x

(2 x + 5) (y^{2} + 4) d x - 4 y (x^{2} + 5 x + 6) d y = 0

\int e^{(a - s) x} d x

What is taylor sin(pi/2-x) ?
The answer to taylor sin(pi/2-x) is 1-1/2 x^2+1/24 x^4-1/720 x^6+1/40320 x^8+\ldots