Pertanyaan

Hitunglah setiap ekspresi berikut. b. sin [ tan − 1 ( − 5 12 ) ]

Hitunglah setiap ekspresi berikut.

b. $sin [tan^{- 1} (- \frac{12}{5})]$

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Klaim

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

.

sin space open square brackets tan to the power of negative 1 end exponent space open parentheses negative 12 over 5 close parentheses close square brackets equals 12 over 13

Pembahasan

Ingat perbandingan sisi trigonometri berikut: Diketahui ekspresi . Misalkan: Perhatikan gambar berikut: Maka: Sehingga: Jadi, .

Ingat perbandingan sisi trigonometri berikut:

$sin space theta equals fraction numerator sisi space depan over denominator sisi space miring end fraction rightwards arrow cosec space theta equals fraction numerator sisi space miring over denominator sisi space depan end fraction cos space theta equals fraction numerator sisi space samping over denominator sisi space miring end fraction rightwards arrow sec space theta equals fraction numerator sisi space miring over denominator sisi space depan end fraction tan space theta equals fraction numerator sisi space depan over denominator sisi space samping end fraction rightwards arrow cotan space theta equals fraction numerator sisi space miring over denominator sisi space depan end fraction$

Diketahui ekspresi sin space open square brackets tan to the power of negative 1 end exponent space open parentheses negative 12 over 5 close parentheses close square brackets . Misalkan:

$table attributes columnalign right center left columnspacing 0px end attributes row theta equals cell tan to the power of negative 1 end exponent space open parentheses negative 12 over 5 close parentheses end cell row cell tan space theta end cell equals cell negative 12 over 5 space rightwards arrow fraction numerator sisi space depan over denominator sisi space samping end fraction end cell end table$

Perhatikan gambar berikut:

Maka:

x equals square root of 12 squared plus 5 squared end root x equals square root of 144 plus 25 end root x equals square root of 169 x equals 13

Sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open square brackets tan to the power of negative 1 end exponent space open parentheses negative 12 over 5 close parentheses close square brackets end cell equals cell sin space theta end cell row blank equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction end cell row blank equals cell 12 over 13 end cell end table$

Jadi, sin space open square brackets tan to the power of negative 1 end exponent space open parentheses negative 12 over 5 close parentheses close square brackets equals 12 over 13 .