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Hitunglah nilai dari tan ( − 4 5 ∘ ) − 2 ( tan 85 5 ∘ ) sin ( − 12 0 ∘ ) + cos ( − 51 0 ∘ ) ​ = ...

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S. Nur

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Diketahui: Operasi sudut trigonometri. Ingatlah kembali rumus Perbandingan trigonometri Sudut-sudut Berelasi, yaitu: Diperoleh: Kemudian operasikan sudut-sudut trigonometrinya seperti berikut: Maka, nilai dari .

Diketahui:

Operasi sudut trigonometri.

Ingatlah kembali rumus Perbandingan trigonometri Sudut-sudut Berelasi, yaitu:

begin mathsize 14px style table attributes columnalign left center right end attributes row cell sin open parentheses 90 degree minus alpha close parentheses end cell equals cell cos space alpha end cell row cell cos open parentheses 90 degree minus alpha close parentheses end cell equals cell sin space alpha end cell row cell tan open parentheses 90 degree minus alpha close parentheses end cell equals cell cot space alpha end cell row cell cot open parentheses 90 degree plus alpha close parentheses end cell equals cell negative tan space alpha end cell row cell tan open parentheses 180 degree minus alpha close parentheses end cell equals cell negative tan space alpha end cell row cell cos open parentheses 180 degree plus alpha close parentheses end cell equals cell negative cos space alpha end cell row cell sin open parentheses 270 degree minus alpha close parentheses end cell equals cell negative cos space alpha end cell row cell sin open parentheses 360 degree plus alpha close parentheses end cell equals cell sin space alpha end cell row cell tan open parentheses 360 degree plus alpha close parentheses end cell equals cell tan space alpha end cell end table end style

Diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses negative 120 degree close parentheses end cell equals cell sin open parentheses 90 degree minus 210 degree close parentheses end cell row blank equals cell cos space 210 degree end cell row cell cos space 210 degree end cell equals cell cos open parentheses 180 degree plus 30 degree close parentheses end cell row blank equals cell negative cos space 30 degree end cell row blank equals cell negative 1 half square root of 3 end cell row blank blank blank row cell cos open parentheses negative 510 degree close parentheses end cell equals cell cos open parentheses 90 degree minus 600 degree close parentheses end cell row blank equals cell sin space 600 degree end cell row cell sin space 600 degree end cell equals cell sin space open parentheses 360 degree plus 240 degree close parentheses end cell row blank equals cell sin space 240 degree end cell row cell sin space 240 degree end cell equals cell sin open parentheses 270 degree minus 30 degree close parentheses end cell row blank equals cell negative cos space 30 degree end cell row blank equals cell negative 1 half square root of 3 end cell row blank blank blank row cell tan open parentheses negative 45 degree close parentheses end cell equals cell tan open parentheses 90 degree minus 135 degree close parentheses end cell row blank equals cell cot space 135 degree end cell row cell cot space 135 degree end cell equals cell cot open parentheses 90 degree plus 45 degree close parentheses end cell row blank equals cell negative tan space 45 degree end cell row blank equals cell negative 1 end cell row blank blank blank row cell tan space 855 degree end cell equals cell tan open parentheses 360 degree plus 495 degree close parentheses end cell row blank equals cell tan space 495 degree end cell row cell tan space 495 degree end cell equals cell tan open parentheses 360 degree plus 135 degree close parentheses end cell row blank equals cell tan space 135 degree end cell row cell tan space 135 degree end cell equals cell tan open parentheses 180 degree minus 45 degree close parentheses end cell row blank equals cell negative tan space 45 degree end cell row blank equals cell negative 1 end cell end table end style

 Kemudian operasikan sudut-sudut trigonometrinya seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin open parentheses negative 120 degree close parentheses plus cos open parentheses negative 510 degree close parentheses over denominator tan open parentheses negative 45 degree close parentheses minus 2 open parentheses tan space 855 degree close parentheses end fraction end cell equals cell fraction numerator negative begin display style 1 half end style square root of 3 plus open parentheses negative 1 half square root of 3 close parentheses over denominator negative 1 minus open parentheses 2 open parentheses negative 1 close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 1 half end style square root of 3 minus 1 half square root of 3 over denominator negative 1 minus open parentheses negative 2 close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 2 over 2 end style square root of 3 over denominator negative 1 plus 2 end fraction end cell row blank equals cell fraction numerator negative square root of 3 over denominator 1 end fraction end cell row blank equals cell negative square root of 3 end cell end table end style

Maka, nilai dari begin mathsize 14px style fraction numerator sin space open parentheses negative 120 degree close parentheses plus cos space open parentheses negative 510 degree close parentheses over denominator tan space open parentheses negative 45 degree close parentheses minus 2 space open parentheses tan space 855 degree close parentheses end fraction equals end stylebegin mathsize 14px style negative square root of 3 end style.

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