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Hitunglah nilai  berikut. a.  ...

Pertanyaan

Hitunglah nilai begin mathsize 14px style Cos end style berikut.
a. begin mathsize 14px style Cos space 660 degree equals end style ...

Pembahasan Soal:

Untuk mendapatkan hasil tersebut, dapat dengan konsep sudut berelasi, sehingga didapat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 660 degree end cell equals cell cos space left parenthesis 2 cross times 360 degree minus 60 degree right parenthesis end cell row blank equals cell cos space left parenthesis negative 60 degree right parenthesis end cell row blank equals cell cos space left parenthesis 60 degree right parenthesis end cell row blank equals cell 1 half end cell end table end style 

Jadi, begin mathsize 14px style cos space 660 to the power of ring operator equals 1 half end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Yoga

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 29 Maret 2021

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Pertanyaan yang serupa

Nilai  adalah ....

Pembahasan Soal:

begin mathsize 14px style tan space 660 degree minus sin space 900 degree plus cos open parentheses negative 390 degree close parentheses equals tan space open parentheses 660 degree minus 360 degree close parentheses minus sin open parentheses 900 degree minus 2 cross times 360 degree close parentheses plus cos open parentheses 390 degree minus 360 degree close parentheses equals tan space 300 degree minus sin space 180 degree plus cos space 30 degree equals negative tan open parentheses 360 degree minus 300 degree close parentheses minus 0 plus 1 half square root of 3 equals negative tan space 60 degree plus 1 half square root of 3 equals negative square root of 3 plus 1 half square root of 3 equals negative 1 half square root of 3 end style 

1

Roboguru

Hitunglah nilai dari  ...

Pembahasan Soal:

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

Sehingga 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.

0

Roboguru

Hitunglah nilai  berikut. b.  ...

Pembahasan Soal:

Untuk mendapatkan nilai tersebut, dapat menggunakan konsep sudut berelasi begin mathsize 14px style left parenthesis 360 degree plus alpha right parenthesis end style, sehingga didapat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses 450 degree close parentheses end cell equals cell cos space open parentheses 360 degree plus 90 degree close parentheses end cell row blank equals cell cos space left parenthesis 90 degree right parenthesis end cell row blank equals 0 end table end style 

Jadi, begin mathsize 14px style cos space open parentheses 450 degree close parentheses equals 0 end style.

0

Roboguru

Jika, maka pernyataan yang tidak benar adalah ....

Pembahasan Soal:

Jika begin mathsize 14px style sin space x equals a end style, maka:

begin mathsize 14px style sin left parenthesis 180 degree plus x right parenthesis equals negative sin space x equals negative a end style 

begin mathsize 14px style sin left parenthesis 360 degree minus x right parenthesis equals negative sin space x equals negative a end style 

begin mathsize 14px style cos left parenthesis 90 degree plus x right parenthesis equals negative sin space x equals negative a end style 

undefined 

begin mathsize 14px style sin space left parenthesis 360 degree plus x right parenthesis equals sin space x equals a end style 

Jadi, Jawaban yang benar adalah C.

0

Roboguru

Tanpa menggunakan tabel atau kalkulator hitunglah nilai dari: i.

Pembahasan Soal:

Perhatikan pehitungan berikut ini.

Ingat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 360 degree plus alpha right parenthesis 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 sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis alpha right parenthesis end cell end table end style

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 390 degree close parentheses end cell equals cell sin space open parentheses 360 degree plus 30 degree close parentheses end cell row blank equals cell sin space open parentheses 30 degree close parentheses end cell row blank equals cell 1 half end cell end table end style

Jadi, nilai begin mathsize 14px style text Sin  end text open parentheses 390 degree close parentheses end style adalah undefined.

0

Roboguru

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