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Jika sin θ + cos θ = 2 3 ​ ​ untuk θ sudut lancipmaka hitunglah: b. sin 3 θ + cos 3 θ

Jika  untuk  sudut lancip maka hitunglah: 

b. 

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari Error converting from MathML to accessible text..

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Pembahasan

Ingat! Diketahui Perhatikan Selanjutnya perhatikan perhitungan berikut: Dengan demikian nilai dari .

Ingat!

sin squared theta plus cos squared theta equals 1

Diketahui

sin space theta plus cos space theta equals fraction numerator square root of 3 over denominator 2 end fraction

Perhatikan

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses sin space theta plus cos space theta close parentheses squared end cell equals cell open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared end cell row cell sin squared theta plus 2 sin space theta space cos space theta plus cos squared theta end cell equals cell 3 over 4 end cell row cell 2 sin space theta space cos space theta plus sin squared theta plus cos squared theta end cell equals cell 3 over 4 end cell row cell 2 sin space theta space cos space theta plus 1 end cell equals cell 3 over 4 end cell row cell 2 sin space theta space cos space theta end cell equals cell 3 over 4 minus 1 end cell row cell 2 sin space theta space cos space theta end cell equals cell negative 1 fourth end cell row cell sin space theta space cos space theta end cell equals cell negative 1 over 8 space space.... space open parentheses 1 close parentheses end cell end table

Selanjutnya perhatikan perhitungan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses sin space theta plus cos space theta close parentheses cubed end cell equals cell open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses cubed end cell row cell sin cubed theta plus 3 sin squared theta cos space theta plus 3 sin space theta cos squared theta plus cos cubed theta end cell equals cell fraction numerator 3 square root of 3 over denominator 8 end fraction end cell row cell sin cubed theta plus cos cubed theta plus 3 sin squared theta cos space theta plus 3 sin space theta cos squared theta end cell equals cell fraction numerator 3 square root of 3 over denominator 8 end fraction end cell row cell sin cubed theta plus cos cubed theta plus 3 sin theta cos space theta open parentheses sin space theta plus cos space theta close parentheses end cell equals cell fraction numerator 3 square root of 3 over denominator 8 end fraction end cell row cell sin cubed theta plus cos cubed theta plus 3 sin theta cos space theta open parentheses sin space theta plus cos space theta close parentheses end cell equals cell fraction numerator 3 square root of 3 over denominator 8 end fraction end cell row cell sin cubed theta plus cos cubed theta plus 3 open parentheses negative 1 over 8 close parentheses open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses end cell equals cell fraction numerator 3 square root of 3 over denominator 8 end fraction end cell row cell sin cubed theta plus cos cubed theta minus fraction numerator 3 square root of 3 over denominator 16 end fraction end cell equals cell fraction numerator 3 square root of 3 over denominator 8 end fraction end cell row cell sin cubed theta plus cos cubed theta end cell equals cell fraction numerator 3 square root of 3 over denominator 8 end fraction plus fraction numerator 3 square root of 3 over denominator 16 end fraction end cell row cell sin cubed theta plus cos cubed theta end cell equals cell fraction numerator 6 square root of 3 over denominator 16 end fraction plus fraction numerator 3 square root of 3 over denominator 16 end fraction end cell row cell sin cubed theta plus cos cubed theta end cell equals cell fraction numerator 9 square root of 3 over denominator 16 end fraction end cell end table

Dengan demikian nilai dari Error converting from MathML to accessible text..

Latihan Bab

Konsep Kilat

Derajat dan Radian

Perbandingan Sisi (Trigonometri)

Sudut Istimewa (Trigonometri)

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