taylor cos^2(θ)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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taylor cos²(θ)

Solution

1−θ²+13 θ⁴−245 θ⁶+1315 θ⁸+…

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Taylor Series

Taylor series of function f(x) at a is defined as:
f(x)=f(a)+f^′(a)1! (x−a)+f^′′(a)2! (x−a)²+f^′′′(a)3! (x−a)³+…

Apply the Taylor Formula

=1+ddθ (cos²(θ))(0)1! θ+d²dθ² (cos²(θ))(0)2! θ²+d³dθ³ (cos²(θ))(0)3! θ³+…

Evaluate Derivatives

=1+01! θ+−22! θ²+03! θ³+84! θ⁴+05! θ⁵+−326! θ⁶+07! θ⁷+1288! θ⁸+…

Refine

=1−θ²+13 θ⁴−245 θ⁶+1315 θ⁸+…

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

taylor cos^2(θ)

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Solution steps

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