Hitunglah dengan menggunakan pemisalan dan teorema...

Pertanyaan

Hitunglah dengan menggunakan pemisalan dan teorema Pythagoras untuk masing-masing ekspresi berikut.

c. $\mathrm{cosec}\;\left[\cos^{-1}\;\left(-\frac{15}{17}\right)\right]$

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

cosec space open square brackets cos to the power of negative 1 end exponent space open parentheses negative 15 over 17 close parentheses close square brackets equals 17 over 8

Pembahasan

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 cosec space open square brackets cos to the power of negative 1 end exponent space open parentheses negative 15 over 17 close parentheses close square brackets . Misalkan:

$table attributes columnalign right center left columnspacing 0px end attributes row theta equals cell cos to the power of negative 1 end exponent space open parentheses negative 15 over 17 close parentheses end cell row cell cos space theta end cell equals cell negative 15 over 17 rightwards arrow fraction numerator sisi space samping over denominator sisi space miring end fraction end cell end table$

Perhatikan gambar berikut:

Maka:

x equals square root of 17 squared minus 15 squared end root x equals square root of 289 minus 225 end root x equals square root of 64 x equals 8

Sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cosec space open square brackets cos to the power of negative 1 end exponent space open parentheses negative 15 over 17 close parentheses close square brackets end cell equals cell cosec space theta end cell row blank equals cell fraction numerator sisi space miring over denominator sisi space depan end fraction end cell row blank equals cell 17 over 8 end cell end table$

Jadi, cosec space open square brackets cos to the power of negative 1 end exponent space open parentheses negative 15 over 17 close parentheses close square brackets equals 17 over 8 .