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Pertanyaan

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4 cos space x degree plus 3 sin space x degree equals 5

Pembahasan Soal:

Dengan mengggunakan rumus trigonometri, misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 cos space x plus 3 sin space x end cell equals cell k cos left parenthesis x plus alpha right parenthesis degree end cell row blank equals cell k cos space x degree times cos space alpha degree plus k sin space x degree times sin space alpha degree end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals 4 row cell k sin space alpha degree end cell equals cell negative 3 end cell row k equals cell square root of open parentheses 4 close parentheses squared plus open parentheses negative 3 close parentheses squared end root end cell row blank equals cell square root of 16 plus 9 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 row cell tan space alpha degree end cell equals cell fraction numerator negative 3 over denominator 4 end fraction space left parenthesis kuadran space IV right parenthesis end cell row cell alpha degree end cell equals cell 323 comma 13 degree end cell end table

Kemudian,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis x plus alpha right parenthesis degree end cell equals cell 5 cos space left parenthesis x plus 323 comma 13 right parenthesis degree equals 5 end cell row blank left right double arrow cell cos space left parenthesis x plus 323 comma 13 right parenthesis degree equals 5 over 5 end cell row cell cos space left parenthesis x plus 323 comma 13 right parenthesis degree end cell equals 1 row cell cos space left parenthesis x plus 323 comma 13 right parenthesis degree end cell equals cell cos space 0 degree end cell row cell space x plus 323 comma 13 degree end cell equals cell 0 degree plus n times 360 degree end cell row x equals cell negative 323 comma 13 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell negative 323 comma 13 degree plus 0 times 360 degree end cell row blank equals cell negative 323 comma 13 degree end cell row x equals cell negative 323 comma 13 degree plus 1 times 360 degree end cell row blank equals cell 36 comma 87 degree end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 36 comma 87 degree close curly brackets end cell end table.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 14 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Selesaikanlah persamaan berikut untuk

Pembahasan Soal:

Dengan mengggunakan rumus trigonometri, misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 cos space 2 x plus 4 sin space 2 x end cell equals cell k cos left parenthesis 2 x plus alpha right parenthesis degree end cell row blank equals cell k cos space 2 x degree times cos space alpha degree minus k sin space 2 x degree times sin space alpha degree end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals 3 row cell k sin space alpha degree end cell equals cell negative 4 end cell row k equals cell square root of open parentheses negative 4 close parentheses squared plus 3 squared end root end cell row blank equals cell square root of 16 plus 9 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 row cell tan space alpha degree end cell equals cell fraction numerator negative 4 over denominator 3 end fraction space left parenthesis kuadran space IV right parenthesis end cell row cell alpha degree end cell equals cell 306 comma 87 degree end cell end table

Kemudian,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis 2 x plus alpha right parenthesis degree end cell equals cell 5 cos space left parenthesis 2 x plus 306 comma 87 right parenthesis degree equals 5 end cell row blank left right double arrow cell cos space left parenthesis 2 x plus 306 comma 87 right parenthesis degree equals 1 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis 2 x plus 306 comma 87 right parenthesis degree end cell equals 1 row cell cos space left parenthesis 2 x plus 306 comma 87 right parenthesis degree end cell equals cell cos space 0 degree end cell row cell space 2 x plus 306 comma 87 degree end cell equals cell 0 degree plus n times 360 degree end cell row cell 2 x end cell equals cell negative 306 comma 87 degree plus n times 360 degree end cell row x equals cell negative 153 comma 435 degree plus n times 180 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 comma space 2 end cell row x equals cell negative 153 comma 435 degree plus 0 times 180 degree end cell row blank equals cell negative 153 comma 435 degree end cell row x equals cell negative 153 comma 435 degree plus 1 times 180 degree end cell row blank equals cell 26 comma 565 degree end cell row x equals cell negative 153 comma 435 degree plus 2 times 180 degree end cell row blank equals cell 206 comma 565 degree end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 26 comma 565 degree comma space 206 comma 565 degree close curly brackets end cell end table.

0

Roboguru

Selesaikanlah persamaan berikut untuk

Pembahasan Soal:

Dengan menggunakan rumus trigonommetri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 sin squared space x plus 4 sin space x times cos space x minus cos squared space x end cell equals 2 row cell 3 sin squared space x plus 2 times 2 sin space x times cos space x minus open parentheses 1 minus sin squared space x close parentheses end cell equals 2 row cell 3 sin squared space x plus 2 sin space 2 x minus 1 plus sin squared space x end cell equals 2 row cell open parentheses negative 2 close parentheses minus 2 sin squared space x plus 2 sin space 2 x end cell equals 3 row cell negative 2 open parentheses cos space 2 x minus 1 close parentheses plus 2 sin space 2 x end cell equals 3 row cell negative 2 cos space 2 x plus 2 plus 2 sin space 2 x end cell equals 3 row cell negative 2 cos space 2 x plus 2 sin space 2 x end cell equals 1 end table

Kemudian misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 cos space 2 x plus 2 sin space 2 x end cell equals cell k cos left parenthesis 2 x plus alpha right parenthesis degree end cell row blank equals cell k cos space 2 x degree times cos space alpha degree minus k sin space 2 x degree times sin space alpha degree end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals cell negative 2 end cell row cell k sin space alpha degree end cell equals cell negative 2 end cell row k equals cell square root of open parentheses negative 2 close parentheses squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 4 plus 4 end root end cell row blank equals cell 2 square root of 2 end cell row cell tan space alpha degree end cell equals cell fraction numerator negative 2 over denominator negative 2 end fraction space left parenthesis kuadran space III right parenthesis end cell row cell alpha degree end cell equals cell 225 degree end cell end table

Kemudian,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis 2 x plus alpha right parenthesis degree end cell equals cell 2 square root of 2 cos space left parenthesis 2 x plus 225 right parenthesis degree equals 1 end cell row blank left right double arrow cell cos space left parenthesis 2 x plus 225 right parenthesis degree equals fraction numerator 1 over denominator 2 square root of 2 end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis 2 x plus 225 right parenthesis degree end cell equals cell fraction numerator 1 over denominator 2 square root of 2 end fraction end cell row cell cos space left parenthesis 2 x plus 225 right parenthesis degree end cell equals cell cos space 69 comma 3 degree end cell row cell space 2 x plus 225 degree end cell equals cell plus-or-minus 69 comma 3 degree plus n times 360 degree end cell row cell 2 x end cell equals cell negative 155 comma 7 degree plus n times 360 degree end cell row x equals cell negative 77 comma 85 degree plus n times 180 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 comma space 2 end cell row x equals cell negative 77 comma 85 degree plus 0 times 180 degree end cell row blank equals cell negative 77 comma 85 degree end cell row x equals cell negative 77 comma 85 degree plus 1 times 180 degree end cell row blank equals cell 102 comma 15 degree end cell row x equals cell negative 77 comma 85 degree plus 2 times 180 degree end cell row blank equals cell 282 comma 15 degree end cell row cell atau space 2 x end cell equals cell negative 294 comma 3 degree plus n times 360 degree end cell row x equals cell negative 147 comma 15 degree plus n times 180 degree end cell row n equals cell 0 comma space 1 comma space 2 end cell row x equals cell negative 147 comma 15 degree plus 0 times 180 degree end cell row blank equals cell negative 147 comma 15 degree end cell row x equals cell negative 147 comma 15 degree plus 1 times 180 degree end cell row blank equals cell 32 comma 85 degree end cell row x equals cell negative 147 comma 15 degree plus 2 times 180 degree end cell row blank equals cell 212 comma 85 degree end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 32 comma 85 degree comma space 102 comma 15 degree comma space 212 comma 85 degree comma space 282 comma 15 degree close curly brackets end cell end table.

0

Roboguru

Himpunan penyelesaian dari persamaan  untuk  adalah...

Pembahasan Soal:

Dengan menggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 6 sin space x plus square root of 2 cos space x end cell equals cell 2 left right double arrow cos x plus square root of 3 sin space x equals square root of 2 end cell end table

Menggunakan rumus k cos open parentheses x minus alpha close parentheses dimana a equals 1 comma space b equals square root of 3 comma space c equals square root of 2,

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space theta end cell equals cell fraction numerator square root of 6 over denominator square root of 2 end fraction end cell row cell tan space theta end cell equals cell square root of 3 end cell row theta equals cell 60 degree end cell end table

k equals square root of 1 squared plus left parenthesis square root of 3 right parenthesis squared end root equals 2

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 cos space left parenthesis x minus 60 degree right parenthesis end cell equals cell square root of 2 end cell row cell cos left parenthesis x minus 60 degree right parenthesis end cell equals cell 1 half square root of 2 end cell row cell cos left parenthesis x minus 60 degree right parenthesis end cell equals cell cos 45 degree end cell row cell x subscript 1 end cell equals cell 60 degree plus 45 degree plus n times 360 degree equals 105 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row cell x subscript 1 end cell equals cell 105 degree plus 0 times 360 degree equals 105 degree end cell row cell x subscript 1 end cell equals cell 105 degree plus 1 times 360 degree equals 465 degree space left parenthesis tidak space memenuhi right parenthesis end cell row blank blank atau row cell x subscript 2 end cell equals cell 60 degree minus 45 degree plus n times 360 degree equals 15 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row cell x subscript 1 end cell equals cell 15 degree plus 0 times 360 degree equals 15 degree end cell row cell x subscript 1 end cell equals cell 15 degree plus 1 times 360 degree equals 375 degree space left parenthesis tidak space memenuhi right parenthesis end cell end table

Dengan demikian,

HP equals open curly brackets 15 degree comma space 105 degree close curly brackets

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Selesaikanlah persamaan berikut untuk

Pembahasan Soal:

Dengan mengggunakan rumus trigonometri, misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 cos space x minus sin space x end cell equals cell k cos left parenthesis x plus alpha right parenthesis degree end cell row blank equals cell k cos space x degree times cos space alpha degree minus k sin space x degree times sin space alpha degree end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals 3 row cell k sin space alpha degree end cell equals 1 row k equals cell square root of 3 squared plus 1 squared end root end cell row blank equals cell square root of 9 plus 1 end root end cell row blank equals cell square root of 10 end cell row cell tan space alpha degree end cell equals cell 1 third space left parenthesis kuadran space straight I right parenthesis end cell row cell alpha degree end cell equals cell 18 comma 43 degree end cell end table

Kemudian,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis x plus alpha right parenthesis degree end cell equals cell square root of 10 cos space left parenthesis x plus 18 comma 43 right parenthesis degree equals square root of 3 end cell row blank left right double arrow cell cos space left parenthesis x plus 18 comma 43 right parenthesis degree equals fraction numerator square root of 3 over denominator square root of 10 end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis x plus 18 comma 43 right parenthesis degree end cell equals cell fraction numerator square root of 3 over denominator square root of 10 end fraction end cell row cell cos space left parenthesis x plus 18 comma 43 right parenthesis degree end cell equals cell cos space 56 comma 79 degree end cell row cell space x plus 18 comma 43 degree end cell equals cell plus-or-minus 56 comma 79 degree plus n times 360 degree end cell row x equals cell 38 comma 36 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell 38 comma 36 degree plus 0 times 360 degree end cell row blank equals cell 38 comma 36 degree end cell row x equals cell 38 comma 36 degree plus 1 times 360 degree end cell row blank equals cell 398 comma 36 degree end cell row cell atau space x end cell equals cell negative 75 comma 22 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell negative 75 comma 22 degree plus 0 times 360 degree end cell row blank equals cell negative 75 comma 22 degree end cell row x equals cell negative 75 comma 22 degree plus 1 times 360 degree end cell row blank equals cell 284 comma 78 degree end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 38 comma 36 degree comma space 284 comma 78 degree close curly brackets end cell end table.

0

Roboguru

Himpunan penyelesaian dari persamaan  untuk  adalah...

Pembahasan Soal:

Dengan mengggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x plus square root of 3 tan space 30 degree end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus square root of 3 times fraction numerator 1 over denominator square root of 3 end fraction end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus 1 end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus 1 end cell equals cell sin 2 times 1 half x end cell row cell cos space x plus 1 end cell equals cell sin x end cell row cell cos space x minus sin space x end cell equals cell negative 1 end cell end table

Misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x minus sin space x end cell equals cell k cos left parenthesis x plus alpha right parenthesis degree end cell row blank equals cell k cos space x degree times cos space alpha degree minus k sin space x degree times sin space alpha degree end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals 1 row cell k sin space alpha degree end cell equals 1 row k equals cell square root of open parentheses 1 close parentheses squared plus open parentheses 1 close parentheses squared end root end cell row blank equals cell square root of 2 end cell row cell tan space alpha degree end cell equals cell 1 over 1 left parenthesis kuadran space straight I right parenthesis end cell row cell alpha degree end cell equals cell 45 degree end cell end table

Kemudian,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis x plus alpha right parenthesis degree end cell equals cell square root of 2 cos space left parenthesis x plus 45 right parenthesis degree equals negative 1 end cell row blank left right double arrow cell cos space left parenthesis x plus 45 right parenthesis degree equals fraction numerator negative 1 over denominator square root of 2 end fraction end cell row cell cos space left parenthesis x plus 45 right parenthesis degree end cell equals cell fraction numerator negative 1 over denominator square root of 2 end fraction end cell row cell cos space left parenthesis x plus 45 right parenthesis degree end cell equals cell cos space 135 degree end cell row cell space x plus 45 degree end cell equals cell plus-or-minus 135 degree plus n times 360 degree end cell row x equals cell 90 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell 90 degree plus 0 times 360 degree end cell row blank equals cell 90 degree end cell row x equals cell 90 degree plus 1 times 360 degree end cell row blank equals cell 450 degree end cell row cell atau space x end cell equals cell negative 180 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell negative 180 degree plus 0 times 360 degree end cell row blank equals cell negative 180 degree end cell row x equals cell negative 180 degree plus 1 times 360 degree end cell row blank equals cell 180 degree end cell end table

Jadi, HP equals open curly brackets 90 degree comma space 180 degree close curly brackets.

Oleh karena itu, jawaban yang benar adalah D.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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