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range of cos^3(t)

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

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≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
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range cos³(t)

Solution

−1≤ f(t)≤ 1

Interval Notation

[−1, 1]

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Function range definition

The set of values of the dependent variable for which a function is defined

Find the minimum and maximum value in each defined interval and unite the results

Domain of cos³(t) : −∞ <t<∞

Extreme Points of cos³(t): Maximum(2πn, 1), Saddle(π2 +2πn, 0), Minimum(π+2πn, −1), Saddle(3π2 +2πn, 0)

Find the range for the interval −∞ <t<∞ : −1≤ f(t)≤ 1

Combine the ranges of all domain intervals to obtain the function range

−1≤ f(t)≤ 1

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domain cos³(t)

periodicity cos³(t)

amplitude cos³(t)

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

range of cos^3(t)

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range of cos^3(t)

Solution

Solution steps

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Number Line

Graph