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Pertanyaan

Hitunglah hasil dari: a. cosec 30 0 ∘ cot 15 0 ∘ ⋅ sec 24 0 ∘ ​

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S. Nur

Master Teacher

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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cot space 150 degree times sec space 240 degree over denominator cosec space 300 degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table.

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Pembahasan

Perhatikan perbandingan trigonometri sudut-sudut berelasi berikut. Sehingga dapat ditentukan nilai dari: Dengan demikian, .

Perhatikan perbandingan trigonometri sudut-sudut berelasi berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 360 degree minus alpha close parentheses end cell equals cell negative sin space alpha end cell row cell cos space open parentheses 270 degree minus alpha close parentheses end cell equals cell negative sin space alpha end cell row cell sin space left parenthesis 180 degree minus alpha right parenthesis end cell equals cell sin space alpha end cell row cell cos space left parenthesis 180 degree minus alpha right parenthesis end cell equals cell negative cos space alpha end cell end table 

Sehingga dapat ditentukan nilai dari:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cot space 150 degree times sec space 240 degree over denominator cosec space 300 degree end fraction end cell equals cell fraction numerator begin display style fraction numerator cos space 150 degree over denominator sin space 150 degree end fraction end style times begin display style fraction numerator 1 over denominator cos space 240 degree end fraction end style over denominator begin display style fraction numerator 1 over denominator sin space 300 degree end fraction end style end fraction end cell row blank equals cell fraction numerator cos space 150 degree times sin space 300 degree over denominator sin space 150 degree times cos space 240 degree end fraction end cell row blank equals cell fraction numerator cos space open parentheses 180 degree minus 30 degree close parentheses times sin space open parentheses 360 degree minus 60 degree close parentheses over denominator sin space open parentheses 180 degree minus 30 degree close parentheses times cos space open parentheses 270 degree minus 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative cos space 30 degree times open parentheses negative sin space 60 degree close parentheses over denominator sin space 30 degree times open parentheses negative sin space 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 1 half end style square root of 3 times open parentheses negative begin display style 1 half end style square root of 3 close parentheses over denominator begin display style 1 half end style times open parentheses negative begin display style 1 half end style close parentheses end fraction end cell row blank equals cell negative 3 end cell end table 

Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cot space 150 degree times sec space 240 degree over denominator cosec space 300 degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table.

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