Pertanyaan

Persamaan garis singgung kurva y = tan x sin x + cos x pada titik dengan absis x = 4 π adalah…

Persamaan garis singgung kurva $y = \frac{sin x + cos x}{tan x}$ pada titik dengan absis $x = \frac{π}{4}$ adalah…

$y equals x plus fraction numerator square root of 2 over denominator 4 end fraction pi plus square root of 2$
$y equals x minus fraction numerator square root of 2 over denominator 4 end fraction pi plus square root of 2$
$y equals square root of 2 x plus fraction numerator square root of 2 over denominator 4 end fraction pi plus square root of 2$
$y equals square root of 2 x minus fraction numerator square root of 2 over denominator 4 end fraction pi plus square root of 2$
$y equals square root of 2 x minus fraction numerator square root of 2 over denominator 4 end fraction pi minus square root of 2$

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Klaim

N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

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Pembahasan

Pertama – tama substitusikan titik x ke persamaan, sehingga didapat:

$begin mathsize 14px style y equals fraction numerator sin pi over 4 plus cos pi over 4 over denominator tan pi over 4 end fraction end style$

$begin mathsize 14px style y equals fraction numerator 1 half square root of 2 plus 1 half square root of 2 over denominator 1 end fraction equals square root of 2 y equals fraction numerator sin space x plus cos space x over denominator tan space x end fraction y to the power of apostrophe equals fraction numerator u to the power of apostrophe v minus u v apostrophe over denominator v squared end fraction y apostrophe equals fraction numerator open parentheses cos space x minus sin space x close parentheses. tan space x plus left parenthesis sin space x plus cos space x right parenthesis sec squared space x over denominator sec squared space x end fraction m equals fraction numerator open parentheses cos space open parentheses pi over 4 close parentheses minus sin space open parentheses pi over 4 close parentheses close parentheses. tan space open parentheses pi over 4 close parentheses plus left parenthesis sin space open parentheses pi over 4 close parentheses plus cos space open parentheses pi over 4 close parentheses right parenthesis sec squared space open parentheses pi over 4 close parentheses over denominator sec squared space open parentheses pi over 4 close parentheses end fraction m equals fraction numerator 2 square root of 2 over denominator 2 end fraction equals square root of 2 Maka comma space persamaan space garis space singgungnya colon y minus square root of 2 equals square root of 2 open parentheses x minus pi over 4 close parentheses y equals square root of 2 x minus fraction numerator square root of 2 over denominator 4 end fraction pi plus square root of 2 end style$

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$\style{font-size:14px}{\mathrm{Garis}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{singgung}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{fungsi}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm y}\style{font-size:14px}=\style{font-size:14px}2\style{font-size:14px}\;\style{font-size:14px}\sin^\style{font-size:14px}2\style{font-size:14px}\;\style{font-size:14px}2\style{font-size:14px}{\mathrm x}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{pada}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{titik}}\\\style{font-size:14px}{\mathrm{yang}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{berabsis}}\style{font-size:14px}\;\frac{\style{font-size:14px}{\mathrm\pi}}{\style{font-size:14px}3}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{akan}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{memotong}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{sumbu}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm Y}\\\style{font-size:14px}{\mathrm{di}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm{titik}}\style{font-size:14px}\;\style{font-size:14px}(\style{font-size:14px}0\style{font-size:14px},\style{font-size:14px}{\mathrm p}\style{font-size:14px})\style{font-size:14px}\;\style{font-size:14px}{\mathrm{maka}}\style{font-size:14px}\;\style{font-size:14px}{\mathrm p}\style{font-size:14px}=\style{font-size:14px}\cdots$

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