Pertanyaan

Hitunglah tanpa menggunakankalkulator atau tabel trigonometri. f. co tan [ sin − 1 ( − 1 ) + cos − 1 ( 2 2 ) ]

Hitunglah tanpa menggunakan kalkulator atau tabel trigonometri.

f. $co tan [sin^{- 1} (- 1) + cos^{- 1} (\frac{2}{2})]$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

.

$c o tan open square brackets sin to the power of negative 1 end exponent open parentheses negative 1 close parentheses plus cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses close square brackets equals negative square root of 2$ .

Pembahasan

Ingat! Jika , maka Jika , maka Akan dicari nilai dari . Dengan demikian, diperoleh Jadi, .

Ingat!

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

Akan dicari nilai dari $c o tan open square brackets sin to the power of negative 1 end exponent open parentheses negative 1 close parentheses plus cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses close square brackets$ .

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses end cell equals y row cell cos space y end cell equals cell fraction numerator square root of 2 over denominator 2 end fraction end cell row y equals cell 45 degree end cell end table$

Dengan demikian, diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell c o tan open square brackets sin to the power of negative 1 end exponent open parentheses negative 1 close parentheses plus cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses close square brackets end cell equals cell c o tan open parentheses x plus y close parentheses end cell row blank equals cell c o tan open parentheses negative 90 degree plus 45 degree close parentheses end cell row blank equals cell c o tan space open parentheses negative 45 degree close parentheses end cell row blank equals cell negative fraction numerator 1 over denominator tan space 45 degree end fraction end cell row blank equals cell negative fraction numerator 1 over denominator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction end cell row blank equals cell negative fraction numerator 2 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell negative square root of 2 end cell end table$

Jadi, $c o tan open square brackets sin to the power of negative 1 end exponent open parentheses negative 1 close parentheses plus cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses close square brackets equals negative square root of 2$ .