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Pertanyaan

sec space 0 degree plus csc space 30 degree equals horizontal ellipsis 

Pembahasan Soal:

Operasi penjumlahan dari fungsi trigonometri dengan sudut berada pada kuadran I dapat diselesaikan seperti berikut :

table attributes columnalign right center left columnspacing 0px end attributes row cell sec space 0 degree plus csc space 30 degree end cell equals cell fraction numerator 1 over denominator cos space 0 degree end fraction plus fraction numerator 1 over denominator sin space 30 degree end fraction end cell row blank equals cell 1 over 1 plus fraction numerator 1 over denominator begin display style 1 half end style end fraction end cell row blank equals cell 1 plus 2 end cell row blank equals 3 end table 

Jadi, hasil dari operasi di atas adalah 3.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 07 Juni 2021

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Pertanyaan yang serupa

Jika  dengan   dan  dengan  sudut  lancip, maka nilai dari  ….

Pembahasan Soal:

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sin invisible function application alpha equals negative 12 over 13  cos invisible function application alpha equals negative 5 over 13

sin invisible function application beta equals 3 over 5  cos invisible function application beta equals 4 over 5    rightwards double arrow sin invisible function application alpha cos invisible function application beta minus cos invisible function application alpha sin invisible function application beta  rightwards double arrow negative 12 over 13 open parentheses 4 over 5 close parentheses minus open parentheses negative 5 over 13 close parentheses open parentheses 3 over 5 close parentheses  rightwards double arrow fraction numerator negative 48 plus 15 over denominator 65 end fraction equals negative 33 over 65

0

Roboguru

Diketahui  dan . Hitung e.

Pembahasan Soal:

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0

Roboguru

Nilai  adalah ...

Pembahasan Soal:

cos space 330 degree space tan left parenthesis negative 315 right parenthesis degree minus sin left parenthesis negative 210 degree right parenthesis space c o t space 330 degree equals 1 half square root of 3 space cross times space 1 space minus 1 half cross times left parenthesis negative square root of 3 right parenthesis equals 1 half square root of 3 space plus 1 half square root of 3 space equals square root of 3

Oleh karena itu, jawaban yang benar adalah D. 

0

Roboguru

Nilai dari  ....

Pembahasan Soal:

Rumus jumlah dua sudut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan 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 open parentheses a degree plus b degree close parentheses 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 cell fraction numerator tan space a degree plus tan space b degree over denominator 1 minus tan space a degree times tan space b degree end fraction end cell end table end style 

 Dalam hal ini, sudut a dan b merupakan sudut-sudut istimewa. Perhatikan bahwa sudut 75° dapat diperoleh dari jumlah dua sudut istimewa seperti yang berikut ini.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 75 degree end cell equals cell tan space open parentheses 45 degree plus 30 degree close parentheses end cell row blank equals cell fraction numerator tan space 45 degree plus tan space 30 degree over denominator 1 minus tan space 45 degree times tan space 30 degree end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 1 third end style square root of 3 over denominator 1 minus open parentheses 1 close parentheses open parentheses 1 third square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator 1 plus 1 third square root of 3 over denominator 1 minus 1 third square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus 1 third square root of 3 over denominator 1 minus 1 third square root of 3 end fraction times fraction numerator 1 plus 1 third square root of 3 over denominator 1 plus 1 third square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 2 over 3 end style square root of 3 plus begin display style 1 third end style over denominator 1 minus 1 third end fraction end cell row blank equals cell fraction numerator begin display style 4 over 3 end style plus begin display style 2 over 3 end style square root of 3 over denominator begin display style 2 over 3 end style end fraction end cell row blank equals cell fraction numerator begin display style 2 over 3 end style open parentheses 2 plus square root of 3 close parentheses over denominator begin display style 2 over 3 end style end fraction end cell row blank equals cell 2 plus square root of 3 end cell end table end style

Jadi, Tan begin mathsize 14px style 75 degree end stylebegin mathsize 14px style equals end style begin mathsize 14px style 2 plus square root of 3 end style

Jadi, jawaban yang tepat adalah A.

0

Roboguru

Nilai dari  adalah ....

Pembahasan Soal:

Ingat!

begin mathsize 14px style tan invisible function application a equals fraction numerator sin invisible function application a over denominator cos invisible function application a end fraction cot invisible function application a equals fraction numerator 1 over denominator tan invisible function application a end fraction equals fraction numerator cos invisible function application a over denominator sin invisible function application a end fraction end style 

Perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 45 degree end cell equals cell 1 half square root of 2 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 135 degree end cell equals cell negative cos invisible function application open parentheses 180 degree minus 45 degree close parentheses end cell row blank equals cell negative cos invisible function application 45 degree end cell row blank equals cell negative 1 half square root of 2 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application 60 degree end cell equals cell fraction numerator sin invisible function application 60 degree over denominator cos invisible function application 60 degree end fraction end cell row blank equals cell fraction numerator 1 half square root of 3 blank over denominator 1 half end fraction end cell row blank equals cell square root of 3 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 225 degree end cell equals cell negative sin invisible function application open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell negative sin invisible function application 45 degree end cell row blank equals cell negative 1 half square root of 2 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 150 degree end cell equals cell negative cos invisible function application open parentheses 180 degree minus 30 degree close parentheses end cell row blank equals cell negative cos invisible function application 30 degree end cell row blank equals cell negative 1 half square root of 3 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cot invisible function application 120 degree end cell equals cell negative cot invisible function application open parentheses 180 degree minus 60 degree close parentheses end cell row blank equals cell negative cot invisible function application 60 degree end cell row blank equals cell negative fraction numerator cos invisible function application 60 degree over denominator sin invisible function application 60 degree end fraction end cell row blank equals cell negative fraction numerator 1 half over denominator 1 half square root of 3 end fraction end cell row blank equals cell negative fraction numerator 1 over denominator square root of 3 end fraction end cell end table end style 

Dengan demikian, diperoleh perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin invisible function application 45 degree cos invisible function application 135 degree tan invisible function application 60 degree over denominator sin invisible function application 225 degree cos invisible function application 150 degree cot invisible function application 120 degree end fraction end cell equals cell fraction numerator open parentheses 1 half square root of 2 close parentheses open parentheses negative 1 half square root of 2 close parentheses open parentheses square root of 3 close parentheses over denominator open parentheses negative 1 half square root of 2 close parentheses open parentheses negative 1 half square root of 3 close parentheses open parentheses negative fraction numerator 1 over denominator square root of 3 end fraction close parentheses end fraction end cell row blank equals cell open parentheses square root of 2 close parentheses open parentheses square root of 3 close parentheses end cell row blank equals cell square root of 6 blank end cell end table end style 

Jadi, jawaban yang tepat adalah A.

0

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