Pertanyaan

Nilai 2 ⋅ sin ( 2 π ) − 2 ⋅ sin ( 6 7 π ) + 4 ⋅ sin ( 4 5 π ) = ...

Nilai $2 \cdot sin (\frac{π}{2}) - 2 \cdot sin (\frac{7 π}{6}) + 4 \cdot sin (\frac{5 π}{4}) = ...$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $2 times sin open parentheses straight pi over 2 close parentheses minus 2 times sin open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses plus 4 times sin open parentheses fraction numerator 5 straight pi over denominator 4 end fraction close parentheses equals 3 minus 2 square root of 2$ .

Pembahasan

Pertama kita konversikan sudut radiannya menjadi derajat. Setelah itu kita cari nilai dari perbandingan trigonometri yang diminta. Jadi nilai dari .

Pertama kita konversikan sudut radiannya menjadi derajat.

$straight pi over 2 rad equals 90 degree fraction numerator 7 straight pi over denominator 6 end fraction rad equals 210 degree fraction numerator 5 straight pi over denominator 4 end fraction r a d equals 225 degree$

Setelah itu kita cari nilai dari perbandingan trigonometri yang diminta.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses straight pi over 2 close parentheses end cell equals cell sin open parentheses 90 degree close parentheses end cell row blank equals 1 end table

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses end cell equals cell sin open parentheses 210 degree close parentheses space space kuadran space III end cell row blank equals cell sin open parentheses 180 degree plus 30 degree close parentheses end cell row blank equals cell negative sin open parentheses 30 degree close parentheses end cell row blank equals cell negative 1 half end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses fraction numerator 5 straight pi over denominator 4 end fraction close parentheses end cell equals cell sin open parentheses 225 degree close parentheses space space space kuadran space III end cell row blank equals cell sin open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell negative sin open parentheses 45 degree close parentheses end cell row blank equals cell negative 1 half square root of 2 end cell end table$

$2 times sin open parentheses straight pi over 2 close parentheses minus 2 times sin open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses plus 4 times sin open parentheses fraction numerator 5 straight pi over denominator 4 end fraction close parentheses equals 2 times 1 minus 2 times open parentheses negative 1 half close parentheses plus 4 times open parentheses negative 1 half square root of 2 close parentheses equals 2 plus 1 minus 2 square root of 2 equals 3 minus 2 square root of 2$

Jadi nilai dari $2 times sin open parentheses straight pi over 2 close parentheses minus 2 times sin open parentheses fraction numerator 7 straight pi over denominator 6 end fraction close parentheses plus 4 times sin open parentheses fraction numerator 5 straight pi over denominator 4 end fraction close parentheses equals 3 minus 2 square root of 2$ .