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Pertanyaan

Nilai dari ekspresi trigonometri, cos space 55 degree times cos space 65 degree plus cos space 65 degree times cos space 175 degree plus cos space 175 degree times cos space 55 degree adalah . . . .

  1. negative 1 comma 0

  2. negative 0 comma 75

  3. negative 0 comma 5

  4. 0 comma 75

  5. 1 comma 00

L. Nikmah

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Ingat rumus perkalian trigonometri serta jumlah dan selisih trigonometri berikut ini:

2 space cos space A space cos space B equals cos space left parenthesis A plus B right parenthesis plus cos space left parenthesis A minus B right parenthesis

cos space A plus cos space B equals 2 space cos space 1 half open parentheses A plus B close parentheses space cos space 1 half open parentheses A minus B close parentheses

Dengan menggunakan konsep di atas, diperoleh hasil:

cos space 55 degree times cos space 65 degree plus cos space 65 degree times cos space 175 degree plus cos space 175 degree times cos space 55 degree equals cos space 65 degree times cos space 55 degree plus cos space 175 degree times cos space 65 degree plus cos space 175 degree times cos space 55 degree equals 1 half open parentheses cos space open parentheses 65 degree plus 55 degree close parentheses plus cos space open parentheses 65 degree minus 55 degree close parentheses close parentheses plus 1 half open parentheses cos space open parentheses 175 degree plus 65 degree close parentheses plus cos space open parentheses 175 degree minus 65 degree close parentheses close parentheses plus 1 half open parentheses cos space open parentheses 175 degree plus 55 degree close parentheses plus cos space open parentheses 175 degree minus 55 degree close parentheses close parentheses equals 1 half open parentheses cos space 120 degree plus cos space 10 degree close parentheses plus 1 half open parentheses cos space 240 degree plus cos space 110 degree close parentheses plus 1 half open parentheses cos space 230 degree plus cos space 120 degree close parentheses equals 1 half open parentheses cos space 120 degree plus cos space 10 degree plus cos space 240 degree plus cos space 110 degree plus cos space 230 degree plus cos space 120 degree close parentheses equals 1 half open parentheses negative 1 half plus cos space 10 degree minus 1 half plus cos space 110 degree plus cos space 230 degree minus 1 half close parentheses equals 1 half open parentheses negative 3 over 2 plus cos space 230 degree plus cos space 110 degree plus cos space 10 degree close parentheses equals 1 half open parentheses negative 3 over 2 plus open parentheses cos space 230 degree plus cos space 110 degree close parentheses plus cos space 10 degree close parentheses equals 1 half open parentheses negative 3 over 2 plus 2 space cos space 1 half open parentheses 230 degree plus 110 degree close parentheses space cos space 1 half open parentheses 230 degree minus 110 degree close parentheses plus cos space 10 degree close parentheses equals 1 half open parentheses negative 3 over 2 plus 2 space cos space 1 half open parentheses 340 degree close parentheses space cos space 1 half open parentheses 120 degree close parentheses plus cos space 10 degree close parentheses equals 1 half open parentheses negative 3 over 2 plus 2 space cos space 170 degree space cos space 60 degree plus cos space 10 degree close parentheses equals 1 half open parentheses negative 3 over 2 plus 2 space cos space 170 degree times 1 half space plus cos space 10 degree close parentheses equals 1 half open parentheses negative 3 over 2 plus cos space 170 degree plus cos space 10 degree close parentheses equals 1 half open parentheses negative 3 over 2 plus 2 space cos space 1 half open parentheses 170 degree plus 10 degree close parentheses space cos space 1 half open parentheses 170 degree minus 10 degree close parentheses space close parentheses equals 1 half open parentheses negative 3 over 2 plus 2 space cos space 1 half open parentheses 180 degree close parentheses space cos space 1 half open parentheses 160 degree close parentheses space close parentheses equals 1 half open parentheses negative 3 over 2 plus 2 space cos space 90 degree space cos space 80 degree space close parentheses equals 1 half open parentheses negative 3 over 2 plus 2 space times 0 times space cos space 80 degree space close parentheses equals 1 half open parentheses negative 3 over 2 plus 0 space close parentheses equals 1 half open parentheses negative 3 over 2 space close parentheses equals negative 3 over 4 equals negative 0 comma 75

Jadi, cos space 55 degree times cos space 65 degree plus cos space 65 degree times cos space 175 degree plus cos space 175 degree times cos space 55 degree equals negative space 0 comma 75.

Oleh karena itu, jawaban yang benar adalah B.

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