Pertanyaan

Hitunglah setiap ekspresi berikut. b, cos [ cos − 1 ( 3 1 ) + cos − 1 ( 4 1 ) ]

Hitunglah setiap ekspresi berikut.

b, $cos [cos^{- 1} (\frac{1}{3}) + cos^{- 1} (\frac{1}{4})]$

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

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Pembahasan

Ingat! Jika , maka Akan dicari nilai dari . Jika , maka Jika , maka Perbandingan trigonometri Jadi, .

Ingat!

Jika cos to the power of negative 1 end exponent space y equals x , maka y equals cos space x

Akan dicari nilai dari cos open square brackets cos to the power of negative 1 end exponent open parentheses 1 third close parentheses plus cos to the power of negative 1 end exponent open parentheses 1 fourth close parentheses close square brackets .

Jika , maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x end cell equals cell samping over miring end cell row blank equals cell 1 third end cell end table

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space italic x end cell equals cell depan over miring end cell row blank equals cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell end table$

Jika , maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space y end cell equals cell samping over miring end cell row blank equals cell 1 fourth end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row depan equals cell square root of miring squared minus sign samping squared end root end cell row blank equals cell square root of 4 squared minus sign 1 squared end root end cell row blank equals cell square root of 16 minus sign 1 end root end cell row blank equals cell square root of 15 end cell end table

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space y end cell equals cell depan over miring end cell row blank equals cell fraction numerator square root of 15 over denominator 4 end fraction end cell end table$

Perbandingan trigonometri

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos open square brackets cos to the power of negative 1 end exponent open parentheses 1 third close parentheses plus cos to the power of negative 1 end exponent open parentheses 1 fourth close parentheses close square brackets end cell equals cell cos open parentheses x plus y close parentheses end cell row blank equals cell cos space x times cos space y minus sin space x times sin space y end cell row blank equals cell 1 third times 1 fourth minus fraction numerator 2 square root of 2 over denominator 3 end fraction times fraction numerator square root of 15 over denominator 4 end fraction end cell row blank equals cell 1 over 12 minus fraction numerator 2 square root of 30 over denominator 12 end fraction end cell row blank equals cell fraction numerator 1 minus 2 square root of 30 over denominator 12 end fraction end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row cell cos open square brackets cos to the power of negative 1 end exponent open parentheses 1 third close parentheses plus cos to the power of negative 1 end exponent open parentheses 1 fourth close parentheses close square brackets end cell equals cell fraction numerator 1 minus 2 square root of 30 over denominator 12 end fraction end cell end table$ .