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Nilai dari tan(−45∘)+sin 120∘+cos 225∘−cos 30∘= ...

Pertanyaan

Nilai dari tan open parentheses negative 45 degree close parentheses plus sin space 120 degree plus cos space 225 degree minus cos space 30 degree equals ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Ubahlah sudut ke dalam bentuk sudut istimewa pada trigonometri.

Gunakan perbandingan trigonometri sudut-sudut berelasi.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 180 degree minus alpha close parentheses end cell equals cell sin space alpha end cell row cell cos space open parentheses 180 degree plus alpha close parentheses end cell equals cell negative cos space alpha end cell end table

Sehingga pada sin space 120 degree dan cos space 225 degree berlaku:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 120 degree end cell equals cell sin space open parentheses 180 degree minus 60 degree close parentheses end cell row blank equals cell sin space 60 degree end cell row blank blank blank row cell cos space 225 degree end cell equals cell cos space open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell negative cos space 45 degree end cell end table

Diperoleh perhitungannya yaitu:

tan open parentheses negative 45 degree close parentheses plus sin space 120 degree plus cos space 225 degree minus cos space 30 degree equals tan open parentheses negative 45 degree close parentheses plus sin space 60 degree plus open parentheses negative cos space 4 5 degree close parentheses minus cos space 30 degree equals negative 1 plus 1 half square root of 3 plus open parentheses negative 1 half square root of 2 close parentheses minus 1 half square root of 3 equals negative 1 plus down diagonal strike 1 half square root of 3 end strike minus 1 half square root of 2 minus down diagonal strike 1 half square root of 3 end strike equals negative 1 minus 1 half square root of 2

Nilai dari tan open parentheses negative 45 degree close parentheses plus sin space 120 degree plus cos space 225 degree minus cos space 30 degree equalsnegative 1 minus 1 half square root of 2.

69

4.5 (2 rating)

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