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Tanpa menggunakan tabel matematika matematika maupun kalkulator, tentukan nilai dari: c. tan 142∘30′

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Tanpa menggunakan tabel matematika matematika maupun kalkulator, tentukan nilai dari:

c. tan space 142 degree 30 apostrophe

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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Pembahasan

Ingat kembali rumus:

tan space open parentheses 90 minus a close parentheses equals negative co tan space a 

cos space straight A equals cos squared straight A over 2 minus sin squared straight A over 2 

tan space open parentheses straight A plus straight B close parentheses equals fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A times tan space straight B end fraction 

sin space left parenthesis straight A minus straight B right parenthesis equals sin space straight A space cos space straight B minus cos space straight A space sin space straight B 

cos space left parenthesis straight A minus straight B right parenthesis equals cos space straight A space cos space straight B plus sin space straight A space sin space straight B 

sin squared straight A plus cos squared straight A equals 1 

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 142 degree 30 apostrophe end cell equals cell tan space 142 comma 5 degree end cell row blank equals cell tan space open parentheses 90 plus 52 comma 5 close parentheses degree end cell row blank equals cell negative cotan space 52 comma 5 degree end cell row blank equals cell fraction numerator negative 1 over denominator tan space 52 comma 5 degree end fraction end cell row blank equals cell fraction numerator negative 1 over denominator tan space open parentheses 45 degree plus 7 comma 5 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative 1 over denominator begin display style fraction numerator tan space 45 degree plus tan space 7 comma 5 degree space over denominator 1 minus tan space 45 degree times tan space 7 comma 5 degree end fraction end style end fraction end cell row blank equals cell fraction numerator negative 1 over denominator begin display style fraction numerator 1 plus tan space 7 comma 5 degree space over denominator 1 minus 1 times tan space 7 comma 5 degree end fraction end style end fraction end cell row blank equals cell negative fraction numerator 1 minus tan space 7 comma 5 degree over denominator 1 plus tan space 7 comma 5 degree space end fraction end cell row blank equals cell negative fraction numerator 1 minus begin display style fraction numerator sin space 7 comma 5 degree over denominator cos space 7 comma 5 degree end fraction end style over denominator 1 plus begin display style fraction numerator sin space 7 comma 5 degree over denominator cos space 7 comma 5 degree end fraction end style end fraction end cell row blank equals cell negative fraction numerator begin display style fraction numerator cos space 7 comma 5 degree minus sin space 7 comma 5 degree over denominator up diagonal strike cos space 7 comma 5 degree end strike end fraction end style over denominator begin display style fraction numerator cos space 7 comma 5 degree plus sin space 7 comma 5 degree over denominator up diagonal strike cos space 7 comma 5 degree end strike end fraction end style end fraction end cell row blank equals cell negative fraction numerator cos space 7 comma 5 degree minus sin space 7 comma 5 degree over denominator cos space 7 comma 5 degree plus sin space 7 comma 5 degree end fraction comma space misalkan space straight A equals 7 comma 5 degree end cell row blank equals cell negative fraction numerator cos space straight A minus sin space straight A over denominator cos space straight A plus sin space straight A end fraction cross times fraction numerator cos space straight A minus sin space straight A over denominator cos space straight A minus sin space straight A end fraction end cell row blank equals cell negative fraction numerator open parentheses cos space straight A minus sin space straight A close parentheses squared over denominator cos squared space straight A minus sin squared space straight A end fraction end cell row blank equals cell negative fraction numerator 1 minus 2 space sin space straight A space cos space straight A over denominator cos squared space straight A minus sin squared space straight A end fraction end cell row blank equals cell negative fraction numerator 1 minus sin space 2 straight A over denominator cos space 2 straight A end fraction end cell row blank equals cell negative fraction numerator 1 minus sin space 2 times 7 comma 5 degree over denominator cos space 2 times 7 comma 5 degree end fraction end cell row blank equals cell negative fraction numerator 1 minus sin space 15 degree over denominator cos space 15 degree end fraction end cell row blank equals cell negative fraction numerator 1 minus sin space open parentheses 45 degree minus 30 degree close parentheses over denominator cos space open parentheses 45 degree minus 30 degree close parentheses end fraction end cell row blank equals cell negative fraction numerator 1 minus open parentheses sin space 45 degree space cos space 30 degree minus cos space 45 degree space sin space 30 degree close parentheses over denominator cos space 45 degree space cos space 30 degree plus sin space 45 degree space sin space 30 degree end fraction end cell row blank equals cell negative fraction numerator 1 minus begin display style fraction numerator square root of 3 minus 1 over denominator 2 square root of 2 end fraction end style over denominator begin display style fraction numerator square root of 3 plus 1 over denominator 2 square root of 2 end fraction end style end fraction end cell row blank equals cell negative fraction numerator 2 square root of 2 minus square root of 3 plus 1 over denominator square root of 3 plus 1 end fraction end cell row blank equals cell negative fraction numerator 2 square root of 2 minus square root of 3 plus 1 over denominator square root of 3 plus 1 end fraction cross times fraction numerator square root of 3 minus 1 over denominator square root of 3 minus 1 end fraction end cell row blank equals cell negative fraction numerator open parentheses 2 square root of 2 minus square root of 3 plus 1 close parentheses open parentheses square root of 3 minus 1 close parentheses over denominator 3 minus 1 end fraction end cell row blank equals cell negative fraction numerator open parentheses 2 square root of 2 open parentheses square root of 3 minus 1 close parentheses minus open parentheses square root of 3 minus 1 close parentheses squared close parentheses over denominator 2 end fraction end cell row blank equals cell negative open square brackets square root of 2 open parentheses square root of 3 minus 1 close parentheses minus open parentheses 2 minus square root of 3 close parentheses close square brackets end cell row blank equals cell negative square root of 6 plus square root of 2 plus 2 minus square root of 3 end cell row blank equals cell 2 plus square root of 2 minus square root of 3 minus square root of 6 end cell end table

 

 Jadi, nilai dari tan space 142 degree 30 apostrophe adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 plus square root of 2 minus square root of 3 minus square root of 6 end cell end table.

 

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