Pertanyaan

tan⁡ 67,5° = ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat bahwa Perhatikan bahwa Perhatikan bahwa sudut 67,5° berada di Kuadran I. Sehingga tan⁡ 67,5°bernilai positif. Maka tan⁡ 67,5° = . Jadi, jawaban yang tepat adalah D.

Ingat bahwa

$begin mathsize 14px style tan invisible function application 1 half A equals plus-or-minus square root of fraction numerator 1 minus cos invisible function application A over denominator 1 plus cos invisible function application A end fraction end root end style$

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application 67 , 5 degree end cell equals cell tan invisible function application 1 half open parentheses 135 degree close parentheses end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus cos invisible function application 135 degree over denominator 1 plus cos invisible function application 135 degree end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus open parentheses negative 1 half square root of 2 close parentheses over denominator 1 plus open parentheses negative 1 half square root of 2 close parentheses end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 plus 1 half square root of 2 over denominator 1 minus 1 half square root of 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 plus 1 half square root of 2 over denominator 1 minus 1 half square root of 2 end fraction times 2 over 2 end root end cell row blank equals cell plus-or-minus square root of fraction numerator 2 plus square root of 2 over denominator 2 minus square root of 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 2 plus square root of 2 over denominator 2 minus square root of 2 end fraction times fraction numerator 2 plus square root of 2 over denominator 2 plus square root of 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 4 plus 4 square root of 2 plus 2 over denominator 4 minus 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 6 plus 4 square root of 2 over denominator 2 end fraction end root end cell row blank equals cell plus-or-minus square root of 3 plus 2 square root of 2 end root end cell end table end style$

Perhatikan bahwa sudut 67,5° berada di Kuadran I. Sehingga tan⁡ 67,5° bernilai positif. Maka tan⁡ 67,5° = .

Jadi, jawaban yang tepat adalah D.