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Nilai  pada persamaan berikut.

Pertanyaan

Nilai  pada persamaan berikut.

x equals fraction numerator sin invisible function application left parenthesis 90 degree plus alpha right parenthesis cos invisible function application open parentheses 90 degree minus alpha close parentheses over denominator cos invisible function application open parentheses 180 degree plus alpha close parentheses end fraction plus fraction numerator sin invisible function application left parenthesis 180 degree minus alpha right parenthesis cos invisible function application open parentheses 90 degree plus alpha close parentheses over denominator sin invisible function application open parentheses 180 degree plus alpha close parentheses end fraction equals

  1. 1 half square root of 3

  2. 1 half

  3. square root of 3

  4. 0

  5. 2

Pembahasan Soal:

space sin invisible function application left parenthesis 90 degree plus alpha right parenthesis equals cos invisible function application alpha  cos invisible function application open parentheses 90 degree minus alpha close parentheses equals sin invisible function application alpha  cos invisible function application open parentheses 180 degree plus alpha close parentheses equals negative cos invisible function application alpha  sin invisible function application open parentheses 180 degree minus alpha close parentheses equals sin invisible function application alpha  cos invisible function application open parentheses 90 degree plus alpha close parentheses equals negative sin invisible function application alpha  sin invisible function application open parentheses 180 degree plus alpha close parentheses equals negative sin invisible function application alpha    fraction numerator sin invisible function application left parenthesis 90 degree plus alpha right parenthesis cos invisible function application open parentheses 90 degree minus alpha close parentheses over denominator cos invisible function application open parentheses 180 degree plus alpha close parentheses end fraction plus fraction numerator sin invisible function application left parenthesis 180 degree minus alpha right parenthesis cos invisible function application open parentheses 90 degree plus alpha close parentheses over denominator sin invisible function application open parentheses 180 degree plus alpha close parentheses end fraction equals fraction numerator cos invisible function application alpha sin invisible function application alpha over denominator negative cos invisible function application alpha end fraction plus fraction numerator sin invisible function application alpha left parenthesis negative sin invisible function application alpha right parenthesis over denominator negative sin invisible function application alpha end fraction  rightwards double arrow negative sin invisible function application alpha plus sin invisible function application alpha equals 0

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Ayu

Mahasiswa/Alumni Universitas Negeri Padang

Terakhir diupdate 15 Desember 2020

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Pertanyaan yang serupa

Tentukan hasil dari cos(261∘−x)+sin(279∘+x)cos(99∘+x)−sin(81∘−x)​=…

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos open parentheses 99 degree plus x close parentheses minus sin left parenthesis 81 degree minus x right parenthesis over denominator cos open parentheses 261 degree minus x close parentheses plus sin left parenthesis 279 degree plus x right parenthesis end fraction end cell equals cell fraction numerator cos open parentheses 90 degree plus 9 degree plus x close parentheses minus sin left parenthesis 90 degree minus 9 degree minus x right parenthesis over denominator cos open parentheses 270 degree minus 9 degree minus x close parentheses plus sin left parenthesis 270 degree plus 9 degree plus x right parenthesis end fraction end cell row blank equals cell fraction numerator cos open parentheses 90 degree plus left parenthesis 9 degree plus x right parenthesis close parentheses minus sin left parenthesis 90 degree minus left parenthesis 9 degree plus x right parenthesis right parenthesis over denominator cos open parentheses 270 degree minus left parenthesis 9 degree plus x right parenthesis close parentheses plus sin left parenthesis 270 degree plus left parenthesis 9 degree plus x right parenthesis right parenthesis end fraction end cell row blank equals cell fraction numerator negative sin open parentheses 9 degree plus x close parentheses minus cos left parenthesis 9 degree plus x right parenthesis over denominator negative sin open parentheses 9 degree plus x close parentheses minus cos left parenthesis 9 degree plus x right parenthesis end fraction end cell row blank equals 1 end table end style 

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Nyatakan dalam bentuk yang paling sederhana. b. cos(90∘+A)+sin(180∘−A)−sin(180∘+A)−sin(−A).

Pembahasan Soal:

Ingat!

cos(90+α)=sin(α)sin(180α)=sin(α)sin(180+α)=sin(α)sin(α)=sin(α) 

Gunakan rumus sudut berelasi, sehingga diperoleh sebagai berikut:

cos(90+A)+sin(180A)sin(180+A)sin(A)=sinA+sinA(sinA)(sinA)=sinA+sinA=2sinA  

Jadi, diperoleh bentuk paling sederhananya adalah begin mathsize 14px style 2 space sin space straight A end style.

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Diketahui segitiga ABC siku-siku di A. Jika cos(A+B)=p, maka nilai sinB+cosC adalah

Pembahasan Soal:

angle straight A space siku minus siku equals 90 degree

cos space left parenthesis straight A plus straight B right parenthesis space equals straight p space  cos space left parenthesis straight A space plus space straight B right parenthesis space equals space cos space left parenthesis 90 degree plus space straight B right parenthesis space equals negative sinB  minus space sinB space equals space straight p space  sin space straight B equals negative straight p space  straight B plus space straight C equals space 90 degree    cos space straight C space equals space cos space left parenthesis 90 degree space minus straight B right parenthesis equals sin space straight B space  sin space straight B plus space cos space straight C equals space sin space straight B plus sin space straight B space  equals space 2 sin space straight B space equals negative 2 straight p

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cos225∘⋅sin45∘⋅cotan250∘sin300∘⋅cos50∘⋅tan160∘​=...

Pembahasan Soal:

Dengan menggunakan rumus sudut berelasi, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space 300 degree times cos space 50 degree times tan space 160 degree over denominator cos space 225 degree times sin space 40 degree times cotan space 250 degree end fraction end cell row blank equals cell fraction numerator sin space 300 degree times cos space open parentheses 90 minus 40 close parentheses degree times tan space open parentheses 90 plus 70 close parentheses degree over denominator cos space 225 degree times sin space 40 degree times cotan space open parentheses 180 plus 70 close parentheses degree end fraction end cell row blank equals cell fraction numerator sin space 300 degree times sin space 40 degree times open parentheses negative cotan space 70 degree close parentheses over denominator cos space 225 degree times sin space 40 degree times cotan space 70 degree end fraction end cell row blank equals cell negative fraction numerator sin space 300 degree over denominator cos space 225 end fraction end cell row blank equals cell negative fraction numerator negative begin display style 1 half end style square root of 3 over denominator negative begin display style 1 half end style square root of 2 end fraction end cell row blank equals cell negative fraction numerator square root of 3 over denominator square root of 2 end fraction end cell row blank equals cell negative 1 half square root of 3 end cell end table 

Jadi,  fraction numerator sin space 300 degree times cos space 50 degree times tan space 160 degree over denominator cos space 225 degree times sin space 45 degree times cotan space 250 degree end fraction equals negative 1 half square root of 3

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tanx⋅sin(90∘−x)cosx⋅tan(90∘+x)​=....

Pembahasan Soal:

Diketahui sudut berelasi dikuadran 1, yaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses 90 degree minus sign italic alpha close parentheses end cell equals cell cos space italic alpha end cell row cell tan open parentheses 90 degree plus italic alpha close parentheses end cell equals cell negative sign italic c italic o tan space italic alpha end cell end table

Dengan demikian, 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space x times tan open parentheses 90 degree plus x close parentheses over denominator tan space x times sin open parentheses 90 degree minus x close parentheses end fraction end cell equals cell fraction numerator cos space x times negative c o tan space x over denominator tan space x times cos space x end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator 1 over denominator tan space x end fraction end style over denominator tan space x end fraction end cell row blank equals cell negative fraction numerator 1 over denominator tan space x end fraction times fraction numerator 1 over denominator tan space x end fraction end cell row blank equals cell negative fraction numerator 1 over denominator tan squared space x end fraction end cell row blank equals cell negative c o tan squared space x end cell end table

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space x times tan open parentheses 90 degree plus x close parentheses over denominator tan space x times sin open parentheses 90 degree minus x close parentheses end fraction end cell equals cell negative c o tan squared space x end cell end table

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Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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