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Hitung nilai tan ( 8 π ​ ) .

Hitung nilai .

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai .

nilai tan space open parentheses straight pi over 8 close parentheses equals square root of 2 minus 1.

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Pembahasan

Ingat kembali: maka: Jadi, nilai .

Ingat kembali:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 1 half straight A end cell equals cell plus-or-minus square root of fraction numerator 1 minus cos space straight A over denominator 1 plus cos space straight A end fraction end root end cell row blank equals cell fraction numerator sin space straight A over denominator 1 plus cos space straight A end fraction end cell row blank equals cell fraction numerator 1 minus cos space straight A over denominator sin space straight A end fraction end cell end table 

maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses straight pi over 8 close parentheses end cell equals cell tan space 22 comma 5 degree end cell row blank equals cell tan space open parentheses 1 half times 45 degree close parentheses end cell row blank equals cell fraction numerator sin space 45 degree over denominator 1 plus cos space 45 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style square root of 2 over denominator 1 plus begin display style 1 half end style square root of 2 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style over denominator begin display style fraction numerator 2 plus square root of 2 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator square root of 2 over denominator up diagonal strike 2 end fraction cross times fraction numerator up diagonal strike 2 over denominator 2 plus square root of 2 end fraction end cell row blank equals cell fraction numerator square root of 2 over denominator 2 plus square root of 2 end fraction cross times fraction numerator 2 minus square root of 2 over denominator 2 minus square root of 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus 2 over denominator 4 minus 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus 2 over denominator 2 end fraction end cell row blank equals cell square root of 2 minus 1 end cell end table 

Jadi, nilai tan space open parentheses straight pi over 8 close parentheses equals square root of 2 minus 1.

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