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Tanpa menggunakan tabel trigonometri maupun kalkulator hitinglah setiap bentuk berikut! sin26∘+sin242∘+sin266+sin278∘

Pertanyaan

Tanpa menggunakan tabel trigonometri maupun kalkulator hitinglah setiap bentuk berikut!

sin squared space 6 degree plus sin squared space 42 degree space plus sin squared space 66 plus sin squared space 78 degree

Pembahasan:

Ingat bahwa :

Sudut berelasi

cos space alpha equals negative cos space open parentheses 180 degree minus alpha close parentheses cos space x equals space sin space open parentheses 90 minus x close parentheses

Sudut rangkap pada sinus 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 2 A end cell equals cell 2 space sin space A space cos space A end cell end table

Sudut rangkap pada cosinus

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 A end cell equals cell 1 minus 2 space sin to the power of 2 space end exponent A end cell row cell 2 space sin to the power of 2 space end exponent A end cell equals cell 1 minus cos space 2 A end cell row cell space sin to the power of 2 space end exponent A end cell equals cell fraction numerator 1 minus cos space 2 A over denominator 2 end fraction end cell row blank blank blank end table

Rumus jumlah dan selisih Trigonometri

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space A minus cos space B space end cell equals cell negative 2 space sin space open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses sin open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses end cell row cell sin space A minus sin space B end cell equals cell 2 space cos space open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses sin open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses end cell end table

Sehingga 

space space space space space sin squared space 6 degree plus sin squared space 42 degree space plus sin squared space 66 plus sin squared space 78 degree equals fraction numerator 1 minus cos space 12 degree over denominator 2 end fraction plus fraction numerator 1 minus cos space 84 degree over denominator 2 end fraction plus fraction numerator 1 minus cos space 132 degree over denominator 2 end fraction plus fraction numerator 1 minus cos space 156 degree over denominator 2 end fraction equals 1 half minus 1 half space cos space 12 degree plus 1 half minus 1 half space cos space 84 degree plus 1 half minus 1 half space cos space 132 degree plus 1 half minus 1 half space cos space 156 degree equals 1 half plus 1 half plus 1 half plus 1 half minus 1 half cos space 12 degree minus 1 half space cos space 84 degree minus 1 half space cos space 132 degree minus 1 half space cos space 156 degree equals 2 minus 1 half cos space 12 degree minus 1 half space cos space 84 degree minus 1 half space cos space 132 degree minus 1 half space cos space 156 degree equals 2 minus 1 half cos space 12 degree minus 1 half space cos space 84 degree plus 1 half space cos space 48 degree plus 1 half space cos space 24 degree equals 2 plus 1 half space cos space 48 degree minus 1 half cos space 12 degree plus 1 half space cos space 24 degree minus 1 half space cos space 84 degree equals 2 plus 1 half open parentheses cos space 48 degree minus cos space 12 degree close parentheses plus 1 half open parentheses cos space 24 degree minus cos space 84 degree close parentheses equals 2 plus 1 half open parentheses negative 2 space sin space 30 degree sin space 18 degree close parentheses plus 1 half open parentheses negative 2 space sin space 54 degree sin space open parentheses negative 30 degree close parentheses close parentheses equals 2 plus 1 half open parentheses negative up diagonal strike 2 open parentheses fraction numerator 1 over denominator up diagonal strike 2 end fraction close parentheses space sin space 18 degree close parentheses plus 1 half open parentheses negative up diagonal strike 2 space sin space 54 degree open parentheses negative fraction numerator 1 over denominator up diagonal strike 2 end fraction close parentheses close parentheses equals 2 minus 1 half sin space 18 degree plus 1 half sin space 54 degree equals 2 plus 1 half open parentheses sin space 54 degree minus sin space 18 degree close parentheses equals 2 plus 1 half open parentheses 2 space cos space 36 degree sin 18 degree close parentheses equals 2 plus 1 half open parentheses 2 space cos space 36 degree sin 18 degree cross times fraction numerator 2 space cos space 18 degree over denominator 2 space cos space 18 degree end fraction close parentheses equals 2 plus 1 half open parentheses fraction numerator 2 space cos space 36 degree space sin 18 degree space 2 cos space 18 degree over denominator 2 space cos space 18 degree end fraction close parentheses equals 2 plus 1 half open parentheses fraction numerator 2 space cos space 36 degree space sin space 36 degree over denominator 2 space cos space 18 degree end fraction close parentheses equals 2 plus 1 half open parentheses fraction numerator space sin space 72 degree over denominator 2 space sin space 72 degree end fraction close parentheses equals 2 plus 1 half open parentheses 1 half close parentheses equals 2 plus 1 fourth equals 2 1 fourth

Dengan demikian nilai dari sin squared space 6 degree plus sin squared space 42 degree space plus sin squared space 66 plus sin squared space 78 degree adalah 2 1 fourth

Jawaban terverifikasi

Dijawab oleh:

I. Roy

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 18 September 2021

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