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Pertanyaan

Jika sin space 2 theta equals 2 sin space theta times cos space theta dan cos space 2 theta equals 1 minus 2 sin squared space theta, hitunglah:

a. cos open parentheses 2 sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses close parentheses

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

 cos open parentheses 2 sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses close parentheses equals 3 over 13.

Pembahasan

Diketahui cos open parentheses 2 sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses close parentheses. Jika cos space 2 theta equals 1 minus 2 sin squared space theta, duperoleh

cos open parentheses 2 sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses close parentheses equals 1 minus sign 2 sin squared open parentheses sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses close parentheses

Jika 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses end cell equals italic theta row cell sin space italic theta end cell equals cell 5 over 13 end cell end table

dan dengan menggunakan prytahgoras diperoleh cos space theta.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space italic theta end cell equals cell depan over miring end cell row blank equals cell 5 over 13 end cell row samping equals cell square root of miring squared minus sign depan squared end root end cell row blank equals cell square root of 13 squared minus sign 5 squared end root end cell row blank equals cell square root of 169 minus sign 25 end root end cell row blank equals cell square root of 144 end cell row blank equals 12 row cell cos space italic theta end cell equals cell samping over miring end cell row blank equals cell 12 over 13 end cell end table

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos open parentheses 2 sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses close parentheses end cell equals cell 1 minus sign 2 sin squared open parentheses sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses close parentheses end cell row blank equals cell 1 minus sign 2 sin squared theta end cell row blank equals cell 1 minus sign 2 middle dot 5 over 13 end cell row blank equals cell 1 minus sign 10 over 13 end cell row blank equals cell fraction numerator 13 minus sign 10 over denominator 13 end fraction end cell row blank equals cell 3 over 13 end cell end table

Jadi, cos open parentheses 2 sin to the power of negative sign 1 end exponent open parentheses 5 over 13 close parentheses close parentheses equals 3 over 13.

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