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Ubahlah titik-titik di bawah ini ke dalam koordina...

Ubahlah titik-titik di bawah ini ke dalam koordinat kutub!

a. begin mathsize 14px style straight A open parentheses 5 comma space 5 square root of 3 close parentheses end style

Jawaban:

Perhatikan perhitungan berikut.

Ingat, koordinat polar:

begin mathsize 14px style straight A open parentheses straight r comma space straight 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

Perhatikan.

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 5 squared plus open parentheses 5 square root of 3 close parentheses squared end root end cell row blank equals cell square root of 25 plus open parentheses 25 times 3 close parentheses end root end cell row blank equals cell square root of 25 plus 75 end root end cell row blank equals cell square root of 100 end cell row blank equals 10 end table end style

Didapatkan begin mathsize 14px style r end style sama dengan begin mathsize 14px style 10 end style. Sehingga:

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 5 over 10 end cell row cell cos space alpha end cell equals cell 1 half end cell row alpha equals cell cos to the power of negative 1 end exponent space 1 half end cell row alpha equals cell 60 degree end cell end table end style

Jadi, koordinat kutub dari koordinat kartesius begin mathsize 14px style straight A open parentheses 5 comma space 5 square root of 3 close parentheses end style adalah begin mathsize 14px style straight A open parentheses 10 comma space 60 degree close parentheses end style.

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