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sin(cos−1(21​3​)) sama dengan ...

Pertanyaan

sin(cos1(213)) sama dengan ...

  1. 3   

  2. 213       

  3. 212    

  4. 1    

  5. 21        

Pembahasan Soal:

Ingat bahwa :

Jika cos1(y) maka cosx=y

sehingga

cos1(213)cosxxsin(cos1(213))====cosx=213cos3030sin3021

Jadi, jawaban yang tepat adalah E

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Roy

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 12 September 2021

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Pertanyaan yang serupa

Lukislah grafik masing-masing fungsi berikut. d,

Pembahasan Soal:

Grafik y equals negative 2 cos to the power of negative 1 end exponent open parentheses x close parentheses

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Lukislah grafik masing-masing fungsi berikut. b,

Pembahasan Soal:

Grafik fungsi y equals cos to the power of negative 1 end exponent open parentheses negative x close parentheses

0

Roboguru

Hitung ekspresi berikut tanpa menggunakan kalkulator maupun tabel trigonometri. b.

Pembahasan Soal:

Ingat kembali nilai-nilai trigonometri pada sudut istimewa berikut:

Diketahui ekspresi s e c a n space open square brackets sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses plus cos to the power of negative 1 end exponent space open parentheses 0 close parentheses plus tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses close square brackets. Misalkan:

- Untuk sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row alpha equals cell sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses end cell row cell sin space alpha end cell equals cell negative 1 half end cell row cell sin space alpha end cell equals cell sin space open parentheses negative 30 degree close parentheses end cell row alpha equals cell negative 30 degree end cell end table 

- Untuk cos to the power of negative 1 end exponent space open parentheses 0 close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row beta equals cell cos to the power of negative 1 end exponent space open parentheses 0 close parentheses end cell row cell cos space beta end cell equals 0 row cell cos space beta end cell equals cell 90 degree end cell row beta equals cell 90 degree end cell end table 

- Untuk tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row gamma equals cell tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses end cell row cell tan space gamma end cell equals cell square root of 3 end cell row cell tan space gamma end cell equals cell tan space 60 degree end cell row gamma equals cell 60 degree end cell end table 

Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell secan space open square brackets sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses plus cos to the power of negative 1 end exponent space open parentheses 0 close parentheses plus tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses close square brackets end cell equals cell secan space open parentheses alpha plus beta plus gamma close parentheses end cell row blank equals cell secan space open parentheses negative 30 degree plus 90 degree plus 60 degree close parentheses end cell row blank equals cell secan space 120 degree end cell row blank equals cell fraction numerator 1 over denominator cos space 120 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator cos space open parentheses 90 degree plus 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative sin space 30 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator negative begin display style 1 half end style end fraction end cell row blank equals cell negative 2 end cell end table end style 

Jadi, secan space open square brackets sin to the power of negative 1 end exponent space open parentheses negative 1 half close parentheses plus cos to the power of negative 1 end exponent space open parentheses 0 close parentheses plus tan to the power of negative 1 end exponent space open parentheses square root of 3 close parentheses close square brackets equals negative 2.

0

Roboguru

Hitunglah dengan menggunakan pemisalan dan teorema Pythagoras untuk masing-masing ekspresi berikut. a.

Pembahasan Soal:

Ingat kembali nilai-nilai trigonometri pada sudut istimewa berikut:

Diketahui ekspresi cotan space open parentheses cos to the power of negative 1 end exponent space fraction numerator square root of 3 over denominator 2 end fraction close parentheses.

Misalkan: cos to the power of negative 1 end exponent space fraction numerator square root of 3 over denominator 2 end fraction equals theta 

Ingat bahwa y equals cos to the power of negative 1 end exponent space x left right double arrow cos space y equals x maka

table attributes columnalign right center left columnspacing 0px end attributes row theta equals cell cos to the power of negative 1 end exponent space fraction numerator square root of 3 over denominator 2 end fraction end cell row cell cos space theta end cell equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell cos space theta end cell equals cell cos space 30 degree end cell row theta equals cell 30 degree end cell end table 

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell cotan space open parentheses cos to the power of negative 1 end exponent space fraction numerator square root of 3 over denominator 2 end fraction close parentheses end cell equals cell c o tan space theta end cell row blank equals cell cotan space 30 degree end cell row blank equals cell square root of 3 end cell end table  

Jadi, cotan space open parentheses cos to the power of negative 1 end exponent space fraction numerator square root of 3 over denominator 2 end fraction close parentheses equals square root of 3.

0

Roboguru

Nilai dari ekspresi: adalah ....

Pembahasan Soal:

Ingat kembali rumus invers fungsi trigonometri berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses cos to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell equals cell square root of 1 minus x squared end root end cell row cell tan space open parentheses sin to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell equals cell fraction numerator x square root of 1 minus x squared end root over denominator 1 minus x squared end fraction end cell end table

Sehingga, diperoleh berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses cos to the power of negative 1 end exponent open parentheses negative 1 third close parentheses close parentheses end cell equals cell square root of 1 minus x squared end root end cell row blank equals cell square root of 1 minus open parentheses negative 1 third close parentheses squared end root end cell row blank equals cell square root of 1 minus 1 over 9 end root end cell row blank equals cell square root of 8 over 9 end root end cell row blank equals cell 1 third square root of 8 end cell row blank equals cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses sin to the power of negative 1 end exponent open parentheses 20 over 29 close parentheses close parentheses end cell equals cell fraction numerator begin display style 20 over 29 end style square root of 1 minus open parentheses begin display style 20 over 29 end style close parentheses squared end root over denominator 1 minus open parentheses begin display style 20 over 29 end style close parentheses squared end fraction end cell row blank equals cell fraction numerator begin display style 20 over 29 end style square root of 1 minus begin display style 400 over 841 end style end root over denominator 1 minus begin display style 400 over 841 end style end fraction end cell row blank equals cell fraction numerator begin display style 20 over 29 square root of 441 over 841 end root end style over denominator begin display style 441 over 841 end style end fraction end cell row blank equals cell fraction numerator begin display style 20 over 29 times bevelled fraction numerator 21 over denominator square root of 841 end fraction end style over denominator begin display style 441 over 841 end style end fraction end cell row blank equals cell fraction numerator begin display style 20 over 29 times 21 over 29 end style over denominator begin display style 441 over 841 end style end fraction end cell row blank equals cell fraction numerator begin display style 420 over 841 end style over denominator begin display style 441 over 841 end style end fraction end cell row blank equals cell fraction numerator 420 over denominator up diagonal strike 841 end fraction cross times fraction numerator up diagonal strike 841 over denominator 441 end fraction end cell row blank equals cell fraction numerator 420 divided by 21 over denominator 441 divided by 21 end fraction end cell row blank equals cell 20 over 21 end cell end table

fraction numerator 2 square root of 2 over denominator 3 end fraction cross times 20 over 21 equals 40 over 63 square root of 2

Dengan demikian, nilai dari ekspresi 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 open parentheses cos to the power of negative 1 end exponent open parentheses negative 1 third close parentheses close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table 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 sin to the power of negative 1 end exponent open parentheses 20 over 29 close parentheses close parentheses end cell end table adalah 40 over 63 square root of 2.

Oleh karena itu, jawaban yang benar adalah A.

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