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Tentukan koordinat kutub dari titik-titik di bawah ini!

Pertanyaan

Tentukan koordinat kutub dari titik-titik di bawah ini!

begin mathsize 14px style left parenthesis negative 3 square root of 5 comma space 4 right parenthesis end style

Pembahasan Soal:

Perhatikan perhitungan berikut ini.

Ingat, koordinat kutub:

begin mathsize 14px style open parentheses r comma space alpha close parentheses end style

dengan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of x squared plus y squared end root end cell row cell cos space alpha end cell equals cell x over r end cell end table end style

Maka:

Titik begin mathsize 14px style left parenthesis negative 3 square root of 5 comma space 4 right parenthesis end style dengan begin mathsize 14px style x equals negative 3 square root of 5 end style dan begin mathsize 14px style y equals 4 end style, sehingga jaraknya:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of x squared plus y squared end root end cell row blank equals cell square root of open parentheses negative 3 square root of 5 close parentheses squared plus 4 squared end root end cell row blank equals cell square root of open parentheses 9 times 5 close parentheses plus 16 end root end cell row blank equals cell square root of 45 plus 16 end root end cell row blank equals cell square root of 61 end cell end table end style

Besar sudut undefined, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell x over r end cell row cell cos space alpha end cell equals cell fraction numerator negative 3 square root of 5 over denominator square root of 61 end fraction end cell row cell cos space alpha end cell equals cell fraction numerator negative 3 square root of 305 over denominator 61 end fraction end cell row alpha equals cell cos to the power of negative 1 end exponent open parentheses fraction numerator negative 3 square root of 305 over denominator 61 end fraction close parentheses end cell row alpha equals cell 149 comma 19 degree end cell end table end style

Jadi, koordinat kutub titik tersebut tersebut adalah begin mathsize 14px style open parentheses square root of 61 comma space 149 comma 19 degree close parentheses end style.

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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