Turito Academy

Test Prep

Global form fields

By fundamental property of f(x) periodic function with period T.<br />f (x+T) =f(x)<br />let f (x) =<img src="data:image/png;base64,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" class="Wirisformula" alt="cos to the power of 6 space x plus sin to the power of 6 space x" width="112" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»cos«/mi»«mn»6«/mn»«/msup»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«msup»«mi»sin«/mi»«mn»6«/mn»«/msup»«mo»§#160;«/mo»«mi»x«/mi»«/math»'/><br />assuming from the options smallest period of f(x) to be <img src="data:image/png;base64,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" class="Wirisformula" alt="pi over 2" width="21" height="31" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»§#960;«/mi»«mn»2«/mn»«/mfrac»«/math»'/>.<br /><img src="data:image/png;base64,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class="Wirisformula" alt="rightwards double arrow f left parenthesis x plus straight pi over 2 right parenthesis equals f left parenthesis x right parenthesis
rightwards double arrow cos to the power of 6 open parentheses x plus straight pi over 2 close parentheses plus sin to the power of 6 open parentheses x plus straight pi over 2 close parentheses equals cos to the power of 6 x plus sin to the power of 6 x
t h e r e f o r e space straight pi over 2 space i s space t h e space f u n d a m e n t a l space p e r i o d space o f space f left parenthesis x right parenthesis.
" width="364" height="123" style="vertical-align:-52px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»2«/mn»«/mfrac»«mo»)«/mo»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mo»§#8658;«/mo»«msup»«mi»cos«/mi»«mn»6«/mn»«/msup»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«mo»+«/mo»«msup»«mi»sin«/mi»«mn»6«/mn»«/msup»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«mo»=«/mo»«msup»«mi»cos«/mi»«mn»6«/mn»«/msup»«mi»x«/mi»«mo»+«/mo»«msup»«mi»sin«/mi»«mn»6«/mn»«/msup»«mi»x«/mi»«mspace linebreak=¨newline¨/»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mi»r«/mi»«mi»e«/mi»«mi»f«/mi»«mi»o«/mi»«mi»r«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mi»i«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mi»a«/mi»«mi»m«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»e«/mi»«mi»r«/mi»«mi»i«/mi»«mi»o«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo».«/mo»«mspace linebreak=¨newline¨/»«/math»'/>

Period of <img src="data:image/png;base64,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" class="Wirisformula" alt="cos to the power of 6 space x plus sin to the power of 6 space x" width="112" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»cos«/mi»«mn»6«/mn»«/msup»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«msup»«mi»sin«/mi»«mn»6«/mn»«/msup»«mo»§#160;«/mo»«mi»x«/mi»«/math»'/> is

Solution for the question - period of cos^(6)x+sin^(6)x is 2pi '/> (3pi)/(2) '/> pi '/> (pi)/(2) '/>