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

Pertanyaan

Diketahui begin mathsize 14px style tan space 25 equals p end style, maka tentukan nilai dari begin mathsize 14px style fraction numerator tan space 205 degree minus tan space 115 degree over denominator tan space 245 degree plus tan space 335 degree end fraction end style

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

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

D. Nuryani

Mahasiswa/Alumni Universitas Padjadjaran

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

cos210∘−cos300∘sin150∘+sin120∘​=…

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 150 degree plus sin space 120 degree over denominator cos space 210 degree minus cos space 300 degree end fraction end cell equals cell fraction numerator sin space open parentheses 90 degree plus 60 degree close parentheses plus sin space open parentheses 90 degree plus 30 degree close parentheses over denominator cos space open parentheses 180 degree plus 30 degree close parentheses minus cos space open parentheses 270 degree plus 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator cos space 60 degree plus cos space 30 degree over denominator negative cos space 30 degree minus sin space 30 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style plus begin display style 1 half end style square root of 3 over denominator negative begin display style 1 half end style square root of 3 minus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half plus 1 half square root of 3 end style over denominator negative open parentheses begin display style 1 half end style square root of 3 plus begin display style 1 half end style close parentheses end fraction end cell row blank equals cell negative 1 end cell end table 

Jadi, fraction numerator sin space 150 degree plus sin space 120 degree over denominator cos space 210 degree minus cos space 300 degree end fraction equals negative 1.

0

Roboguru

Jikasinx=a, 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 

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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.

0

Roboguru

Tentukan nilai dari cos210∘−cos300∘sin150∘+sin120∘​.

Pembahasan Soal:

Gunakanlah sudut berelasi untuk menjawab soal di atas.

Ingat!

  • Nilai sin pada kuadran II adalah positif, sedangkan nilai cos dan tan negatif.
  • Nilai tan pada kuadran III positif, sedangkan nilai sin dan cos negatif.
  • Nilai cos  pada kuadran IV positif, sedangkan nilai sin dan tan negatif.

Berdasarkan nilai trigonometri pada kuadran II, III, dan IV di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 150 degree plus sin space 120 degree over denominator cos space 210 degree minus cos space 300 degree end fraction end cell equals cell fraction numerator sin open parentheses 180 degree minus 30 degree close parentheses plus sin open parentheses 180 degree minus 60 degree close parentheses over denominator cos open parentheses 180 degree plus 30 degree close parentheses minus cos open parentheses 360 degree minus 60 degree close parentheses end fraction end cell row blank equals cell fraction numerator sin space 30 degree plus sin space 60 degree over denominator negative cos space 30 degree minus cos space 60 degree end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style plus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style over denominator negative begin display style fraction numerator square root of 3 over denominator 2 end fraction end style minus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style 1 half plus fraction numerator square root of 3 over denominator 2 end fraction end style over denominator negative open parentheses begin display style 1 half end style plus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell negative 1. end cell end table  

Dengan demikian, nilai dari fraction numerator sin space 150 degree plus sin space 120 degree over denominator cos space 210 degree minus cos space 300 degree end fraction adalah negative 1.

0

Roboguru

Nilai dari sin150∘+4⋅cos330∘−tg225∘

Pembahasan Soal:

Nilai sinus pada sudut berelasi di kuadran II, yaitu

sin space open parentheses 180 degree minus alpha close parentheses equals sin space alpha

Nilai tangen pada sudut berelasi di kuadran III, yaitu

tan space open parentheses 180 degree plus alpha close parentheses equals tan space alpha

Nilai cosinus pada sudut berelasi di kuadran IV, yaitu

cos space open parentheses 360 degree minus alpha close parentheses equals cos space alpha

Berdasarkan konsep di atas, dapat ditentukan nilai trigonometri dari berbagai kuadran berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 150 degree end cell equals cell sin space open parentheses 180 degree minus 30 degree close parentheses end cell row blank equals cell sin space 30 degree end cell row blank equals cell 1 half end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 330 degree end cell equals cell cos space open parentheses 360 degree minus 30 degree close parentheses end cell row blank equals cell cos space 30 degree end cell row blank equals cell 1 half square root of 3 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell t g space 225 degree end cell equals cell t g space open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell t g space 45 degree end cell row blank equals 1 end table

Hasil dari operasi hitung nilai trigonometri tersebut adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin space 150 degree plus 4 times cos space 330 degree minus t g space 225 degree end cell row blank equals cell 1 half plus 4 times 1 half square root of 3 minus 1 end cell row blank equals cell 2 square root of 3 minus 1 half end cell end table

Dengan demikian, nilai 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 150 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos 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 330 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank t end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank g 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 225 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half 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

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