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Nilai sin 20 0 ∘ ⋅ cos 10 0 ∘ + cos 20 0 ∘ ⋅ sin 10 0 ∘ adalah ....

Nilai  adalah ....

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P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

.

 sin space 200 degree times cos space 100 degree plus cos space 200 degree times sin space 100 degree equals negative 1 half square root of 3.

Pembahasan

Akan dicari nilai dari dan . Maka diperoleh: Dengan demikian, .

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 200 degree times cos space 100 degree end cell equals cell 1 half open square brackets sin open parentheses 200 degree plus 100 degree close parentheses plus sin open parentheses 200 degree minus 100 degree close parentheses close square brackets end cell row blank equals cell 1 half open parentheses sin space 300 degree plus sin space 100 degree close parentheses end cell end table 

Akan dicari nilai dari sin space 300 degree dan sin space 100 degree.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 300 degree end cell equals cell sin open parentheses 360 degree minus 60 degree close parentheses end cell row blank equals cell negative sin space 60 degree end cell row blank equals cell negative 1 half square root of 3 end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 100 degree end cell equals cell sin open parentheses 90 degree plus 10 degree close parentheses end cell row blank equals cell sin space 90 degree times cos space 10 degree plus cos space 90 degree times sin space 90 degree end cell row blank equals cell cos space 10 degree plus 0 end cell row blank equals cell cos space 10 degree end cell end table 

Maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 200 degree times cos space 100 degree end cell equals cell 1 half open square brackets sin open parentheses 200 degree plus 100 degree close parentheses plus sin open parentheses 200 degree minus 100 degree close parentheses close square brackets end cell row blank equals cell 1 half open parentheses sin space 300 degree plus sin space 100 degree close parentheses end cell row blank equals cell 1 half open parentheses negative 1 half square root of 3 plus space cos space 10 degree close parentheses end cell row blank equals cell negative 1 fourth square root of 3 plus 1 half cos space 10 degree end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 200 degree times sin space 100 degree end cell equals cell 1 half open square brackets sin open parentheses 200 degree plus 100 degree close parentheses minus sin open parentheses 200 degree minus 100 degree close parentheses close square brackets end cell row blank equals cell 1 half open parentheses sin space 300 degree minus sin space 100 degree close parentheses end cell row blank equals cell 1 half open parentheses negative 1 half square root of 3 minus space cos space 10 degree close parentheses end cell row blank equals cell negative 1 fourth square root of 3 minus 1 half cos space 10 degree end cell end table 

sin space 200 degree times cos space 100 degree plus cos space 200 degree times sin space 100 degree equals negative 1 fourth square root of 3 plus 1 half cos space 10 degree minus 1 fourth square root of 3 minus 1 half cos space 10 degree equals negative 2 over 4 square root of 3 equals negative 1 half square root of 3 

Dengan demikian, sin space 200 degree times cos space 100 degree plus cos space 200 degree times sin space 100 degree equals negative 1 half square root of 3.

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