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Jikasinx=a, maka pernyataan yang tidak benar adalah ....

Pertanyaan

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

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Pembahasan Video:

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 

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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.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Wati

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Hitunglah nilai dari tan(−45∘)−2(tan855∘)sin(−120∘)+cos(−510∘)​= ...

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

Diketahui tan25=p, maka tentukan nilai dari tan245∘+tan335∘tan205∘−tan115∘​

Pembahasan Soal:

Menggunakan konsep sudut berelasi di kuadran II, III, IV.

Sehingga, penyelesaiannya adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space 205 to the power of degree minus tan space 115 to the power of degree over denominator tan space 245 to the power of degree plus tan space 335 to the power of degree end fraction end cell equals cell fraction numerator tan left parenthesis 180 to the power of degree plus 25 to the power of degree right parenthesis minus tan open parentheses 90 to the power of degree plus 25 to the power of degree close parentheses over denominator tan open parentheses 270 to the power of degree minus 25 to the power of degree close parentheses plus tan open parentheses 360 to the power of degree minus 25 to the power of degree close parentheses end fraction end cell row blank equals cell fraction numerator tan space 25 to the power of degree plus text cot end text space 25 to the power of degree over denominator text cot end text space 25 to the power of degree minus tan space 25 to the power of degree end fraction end cell row blank equals cell fraction numerator p plus begin display style 1 over p end style over denominator begin display style 1 over p end style minus p end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator p squared plus 1 over denominator p end fraction end style over denominator begin display style fraction numerator 1 minus p squared over denominator p end fraction end style end fraction end cell row blank equals cell fraction numerator p squared plus 1 over denominator 1 minus p squared end fraction end cell end table end style
 

Jadi, jika diketahui begin mathsize 14px style tan space 25 equals p end style maka nilai dari fraction numerator tan space 205 degree minus tan space 115 degree over denominator tan space 245 degree plus tan space 335 degree end fraction equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator p squared plus 1 over denominator 1 minus p squared end fraction end cell end table

0

Roboguru

Bentuk sederhana dari cosec(180∘+x)tan(90∘−x)cot(90∘+x)sec(270∘−x)​ adalah ....

Pembahasan Soal:

Perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cot left parenthesis 90 degree plus x right parenthesis sec left parenthesis 270 degree minus x right parenthesis over denominator cosec left parenthesis 180 degree plus x right parenthesis tan left parenthesis 90 degree minus x right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis negative tan x right parenthesis left parenthesis negative cosec x right parenthesis over denominator left parenthesis negative cosec x right parenthesis left parenthesis cot x right parenthesis end fraction end cell row blank equals cell fraction numerator negative tan x over denominator cot x end fraction end cell row blank equals cell fraction numerator negative tan x over denominator begin display style fraction numerator 1 over denominator tan x end fraction end style end fraction end cell row blank equals cell negative tan x times tan x end cell row blank equals cell negative tan squared x end cell end table end style

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Nilai ( cosec 315°+sec 225°)-cotan2120∘ adalah ....

Pembahasan Soal:

begin mathsize 14px style open parentheses cosec space 315 degree plus sec space 225 degree close parentheses minus cotan squared space 120 degree equals open parentheses cosec open parentheses 360 degree minus 45 degree close parentheses plus sec open parentheses 180 degree plus 45 degree close parentheses close parentheses minus cotan squared space open parentheses 180 degree minus 60 degree close parentheses equals open parentheses negative cosec space 45 degree plus open parentheses negative sec space 45 degree close parentheses close parentheses minus open parentheses negative cotan squared space 60 degree close parentheses equals open parentheses negative fraction numerator 2 over denominator square root of 2 end fraction minus fraction numerator 2 over denominator square root of 2 end fraction close parentheses plus open parentheses fraction numerator 1 over denominator square root of 3 end fraction close parentheses squared equals negative fraction numerator 4 over denominator square root of 2 end fraction plus 1 third equals negative 2 square root of 2 plus 1 third equals fraction numerator negative 6 square root of 2 plus 1 over denominator 3 end fraction end style 

1

Roboguru

Diketahui cotan (90∘−θ)°=43​. Hitunglah nilai cosec(180+θ)∘+sec(270−θ)∘+cos(360−θ)∘!

Pembahasan Soal:

Misalkan: text cosec end text space open parentheses 180 plus theta close parentheses degree plus text sec end text space open parentheses 270 minus theta close parentheses degree plus cos space open parentheses 360 minus theta close parentheses degree equals L

Dengan menggunakan aturan pada trigonometri, maka berlaku:

table attributes columnalign right center left columnspacing 0px end attributes row cell text cotan end text space open parentheses 90 degree minus theta close parentheses end cell equals cell tan space open parentheses theta close parentheses end cell row cell text cosec  end text open parentheses 180 degree plus theta close parentheses end cell equals cell negative space text cosec  end text open parentheses theta close parentheses end cell row cell text sec end text space open parentheses 270 degree minus theta close parentheses end cell equals cell negative space text cosec  end text open parentheses theta close parentheses end cell row cell text cos end text space open parentheses 360 degree minus theta close parentheses end cell equals cell cos space open parentheses theta close parentheses end cell row cell tan space open parentheses theta close parentheses end cell equals cell fraction numerator sin space open parentheses theta close parentheses over denominator cos space open parentheses theta close parentheses end fraction end cell end table  

Karena, nilai dari text cotan  end text open parentheses 90 minus theta close parentheses text ° end text equals 3 over 4, maka nilai dari tan space open parentheses theta close parentheses equals 3 over 4.

Perhatikan gambar berikut! 

Dari gambar di atas, maka diperoleh nilai dari sin space open parentheses theta close parentheses equals 3 over 5 dan cos space open parentheses theta close parentheses equals 4 over 5.

Selanjutnya, akan dicari nilai dari left parenthesis L right parenthesis pada soal di atas dengan menggunakan nilai dari sin space open parentheses theta close parentheses dan cos space open parentheses theta close parentheses yang telah diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row L equals cell text cosec end text space open parentheses 180 plus theta close parentheses degree plus text sec end text space open parentheses 270 minus theta close parentheses degree plus cos space open parentheses 360 minus theta close parentheses degree end cell row blank equals cell negative space text cosec end text space open parentheses theta close parentheses space minus space text cosec end text space open parentheses theta close parentheses space plus cos space open parentheses theta close parentheses end cell row blank equals cell negative 2 space text cosec end text space open parentheses theta close parentheses space plus cos space open parentheses theta close parentheses end cell row blank equals cell negative 2 space open parentheses fraction numerator 1 over denominator sin space open parentheses theta close parentheses end fraction close parentheses plus cos space open parentheses theta close parentheses end cell row blank equals cell negative 2 space open parentheses fraction numerator 1 over denominator begin display style 3 over 5 end style end fraction close parentheses plus 4 over 5 end cell row blank equals cell negative 2 times 5 over 3 plus 4 over 5 end cell row blank equals cell fraction numerator negative 10 over denominator 3 end fraction plus 4 over 5 end cell row blank equals cell fraction numerator negative 50 plus 12 over denominator 15 end fraction end cell row L equals cell negative 38 over 15 end cell end table 

Dengan demikian, nilai dari text cosec end text space open parentheses 180 plus theta close parentheses degree plus text sec end text space open parentheses 270 minus theta close parentheses degree plus cos space open parentheses 360 minus theta close parentheses degree adalah negative 38 over 15. 

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