Pertanyaan

Hitunglah dengan menggunakan pemisalan dan teorema Pythagoras untuk masing-masing ekspresi berikut. b. secan [ sin − 1 ( 7 4 ) ]

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

b. $secan [sin^{- 1} (\frac{4}{7})]$

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

.

$secan space open square brackets sin to the power of negative 1 end exponent space open parentheses 4 over 7 close parentheses close square brackets equals fraction numerator 7 over denominator square root of 33 end fraction$ .

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 secan space open square brackets sin to the power of negative 1 end exponent space open parentheses 4 over 7 close parentheses close square brackets . Misalkan:

$table attributes columnalign right center left columnspacing 0px end attributes row theta equals cell sin to the power of negative 1 end exponent space open parentheses 4 over 7 close parentheses end cell row cell sin space theta end cell equals cell 4 over 7 rightwards arrow fraction numerator sisi space depan over denominator sisi space miring end fraction end cell end table$

Perhatikan gambar berikut:

Maka:

x equals square root of 7 squared minus 4 squared end root x equals square root of 49 minus 16 end root x equals square root of 33

Sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell secan space open square brackets sin to the power of negative 1 end exponent space open parentheses 4 over 7 close parentheses close square brackets end cell equals cell sec space theta end cell row blank equals cell fraction numerator sisi space miring over denominator sisi space samping end fraction end cell row blank equals cell fraction numerator 7 over denominator square root of 33 end fraction end cell end table$

Jadi, $secan space open square brackets sin to the power of negative 1 end exponent space open parentheses 4 over 7 close parentheses close square brackets equals fraction numerator 7 over denominator square root of 33 end fraction$ .