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Hitunglah nilai dari: cos 300∘+tan 330∘+sin 360∘sin 150∘+tan 225∘−cos 120∘​

Pertanyaan

Hitunglah nilai dari:

fraction numerator sin space 150 degree plus tan space 225 degree minus cos space 120 degree over denominator cos space 300 degree plus tan space 330 degree plus sin space 360 degree end fraction

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai dari fraction numerator sin space 150 degree plus tan space 225 degree minus cos space 120 degree over denominator cos space 300 degree plus tan space 330 degree plus sin space 360 degree end fraction adalah negative 12 minus 8 square root of 3.

Pembahasan

Ingat bahwa untuk setiap alpha lancip, maka open parentheses 90 degree plus alpha close parentheses dan open parentheses 180 degree minus alpha close parentheses akan menghasilkan sudut kuadran II, open parentheses 180 degree plus alpha close parentheses akan menghasilkan sudut kuadran III, dan open parentheses 360 degree minus alpha close parentheses akan menghasilkan sudut kuadran IV.

Oleh karena itu, akan diperoleh nilai dari fraction numerator sin space 150 degree plus tan space 225 degree minus cos space 120 degree over denominator cos space 300 degree plus tan space 330 degree plus sin space 360 degree end fraction adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 150 degree plus tan space 225 degree minus cos space 120 degree over denominator cos space 300 degree plus tan space 330 degree plus sin space 360 degree end fraction end cell row blank equals cell fraction numerator sin space open parentheses 180 degree minus 30 degree close parentheses plus tan space open parentheses 180 degree plus 45 degree close parentheses minus cos space open parentheses 180 degree minus 60 degree close parentheses over denominator cos space open parentheses 360 degree minus 60 degree close parentheses plus tan space open parentheses 360 degree minus 30 degree close parentheses plus sin space open parentheses 360 degree minus 0 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin space open parentheses 30 degree close parentheses plus tan space open parentheses 45 degree close parentheses minus open parentheses negative cos space open parentheses 180 degree minus 60 degree close parentheses close parentheses over denominator cos space open parentheses 60 degree close parentheses minus tan space open parentheses 30 degree close parentheses minus sin space open parentheses 0 degree close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style plus 1 plus begin display style 1 half end style over denominator begin display style 1 half end style minus square root of 3 minus 0 end fraction end cell row blank equals cell fraction numerator begin display style 2 end style over denominator begin display style 1 half minus 1 third square root of 3 end style end fraction cross times fraction numerator begin display style 1 half plus 1 third square root of 3 end style over denominator begin display style 1 half plus 1 third square root of 3 end style end fraction end cell row blank equals cell fraction numerator 1 plus 2 over 3 square root of 3 over denominator begin display style 1 fourth end style minus begin display style 1 third end style end fraction end cell row blank equals cell fraction numerator 1 plus 2 over 3 square root of 3 over denominator begin display style negative 1 over 12 end style end fraction end cell row blank equals cell negative 12 open parentheses 1 plus 2 over 3 square root of 3 close parentheses end cell row blank equals cell negative 12 minus 8 square root of 3 end cell end table

Dengan demikian, nilai dari fraction numerator sin space 150 degree plus tan space 225 degree minus cos space 120 degree over denominator cos space 300 degree plus tan space 330 degree plus sin space 360 degree end fraction adalah negative 12 minus 8 square root of 3.

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