Pertanyaan

Jika sin 2 θ = 2 sin θ ⋅ cos θ dan cos 2 θ = 1 − 2 sin 2 θ , hitunglah: a. cos ( 2 sin − 1 ( 13 5 ) )

Jika $sin 2 θ = 2 sin θ \cdot cos θ$ dan $cos 2 θ = 1 - 2 sin^{2} θ$ , hitunglah:

a. $cos (2 sin^{- 1} (\frac{5}{13}))$

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 . Jika , duperoleh Jika dan dengan menggunakan prytahgoras diperoleh . maka Jadi, .

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 .

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 .