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Tentukan nilai-nilai perbandingan trigonometri pada titik berikut! d.

Pertanyaan

Tentukan nilai-nilai perbandingan trigonometri pada titik berikut!

d. straight D left parenthesis negative 8 comma negative 12 right parenthesis 

Pembahasan Soal:

Diketahui titik straight D left parenthesis negative 8 comma negative 12 right parenthesis artinya x equals negative 8 space dan space y equals negative 12, maka dapat kita cari panjang sisi miring left parenthesis r right parenthesis dengan menggunakan pythagoras.

table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of x squared plus y squared end root end cell row blank equals cell square root of left parenthesis negative 8 right parenthesis squared plus left parenthesis negative 12 right parenthesis to the power of 2 end exponent end root end cell row blank equals cell square root of 64 plus 144 end root end cell row blank equals cell square root of 208 end cell row blank equals cell square root of 16 cross times 13 end root end cell row blank equals cell 4 square root of 13 end cell end table 

Akan ditentukan sinus dari D

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight D end cell equals cell y over r end cell row blank equals cell fraction numerator negative 12 over denominator 4 square root of 13 end fraction end cell row blank equals cell negative fraction numerator 12 over denominator 4 square root of 13 end fraction cross times fraction numerator square root of 13 over denominator square root of 13 end fraction end cell row blank equals cell negative fraction numerator 12 square root of 13 over denominator 4 cross times 13 end fraction end cell row blank equals cell negative fraction numerator 12 square root of 13 over denominator 52 end fraction end cell end table 

Jadi, nilai sinus dari D adalah negative fraction numerator 12 square root of 13 over denominator 52 end fraction.

Akan ditentukan cosinus dari D

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight D end cell equals cell x over r end cell row blank equals cell fraction numerator negative 8 over denominator 4 square root of 13 end fraction end cell row blank equals cell negative fraction numerator 8 over denominator 4 square root of 13 end fraction cross times fraction numerator square root of 13 over denominator square root of 13 end fraction end cell row blank equals cell negative fraction numerator 8 square root of 13 over denominator 4 cross times 13 end fraction end cell row blank equals cell negative fraction numerator 8 square root of 13 over denominator 52 end fraction end cell end table 

Jadi, nilai cosinus dari D adalah negative fraction numerator 8 square root of 13 over denominator 52 end fraction.

Akan ditentukan tangen dari D

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight D end cell equals cell y over x end cell row blank equals cell fraction numerator negative 12 over denominator negative 8 end fraction end cell row blank equals cell 12 over 8 end cell end table 

Jadi, nilai tangen dari D adalah 12 over 8.

Akan ditentukan cosecan dari D

table attributes columnalign right center left columnspacing 0px end attributes row cell csc space straight D end cell equals cell r over y end cell row blank equals cell fraction numerator 4 square root of 13 over denominator negative 12 end fraction end cell row blank equals cell negative fraction numerator 4 square root of 13 over denominator 12 end fraction end cell end table 

Jadi, nilai cosecan dari D adalah negative fraction numerator 4 square root of 13 over denominator 12 end fraction.

Akan ditentukan secan dari D

table attributes columnalign right center left columnspacing 0px end attributes row cell sec space straight D end cell equals cell r over x end cell row blank equals cell fraction numerator 4 square root of 13 over denominator negative 8 end fraction end cell row blank equals cell negative fraction numerator 4 square root of 13 over denominator 8 end fraction end cell end table 

Jadi, nilai secan dari D adalah negative fraction numerator 4 square root of 13 over denominator 8 end fraction.

Akan ditentukan cotangen dari D

table attributes columnalign right center left columnspacing 0px end attributes row cell cot space straight D end cell equals cell x over y end cell row blank equals cell fraction numerator negative 8 over denominator negative 12 end fraction end cell row blank equals cell 8 over 12 end cell end table 

Jadi, nilai cotangen dari D adalah 8 over 12.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Lestari

Mahasiswa/Alumni Universitas Sebelas Maret

Terakhir diupdate 04 Juni 2021

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Pertanyaan yang serupa

Lengkapi tabel berikut!

Pembahasan Soal:

Dapat diketahui bahwa nilai begin mathsize 14px style sin space 45 degree equals 1 half square root of 2 end style dan begin mathsize 14px style cos space 45 degree equals 1 half square root of 2 end style, sehingga berdasarkan informasi pada tabel dapat dibentuk segitiga siku-siku sebagai berikut.

Sehingga dapat dilengkapi tabel di atas sebagai berikut.

0

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Tentukan nilai dari keenam perbandingan trigonometri sudut  pada segitiga siku-siku berikut.

Pembahasan Soal:

Kita cari sisi miring nya

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell sisi space miring end cell equals cell square root of 6 squared plus 8 squared end root end cell row blank equals cell square root of 36 plus 64 end root end cell row blank equals cell square root of 100 end cell row blank equals 10 end table end style 

perbandingan trigonometri sudut begin mathsize 14px style straight alpha end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell sin space straight alpha end cell equals cell de over mi equals 6 over 10 end cell row cell cos space straight alpha end cell equals cell sa over mi equals 8 over 10 end cell row cell tan space straight alpha end cell equals cell de over sa equals 6 over 8 end cell row cell cossec space straight alpha end cell equals cell fraction numerator 1 over denominator sin space straight alpha end fraction equals 10 over 6 end cell row cell sec space straight alpha end cell equals cell fraction numerator 1 over denominator cos space straight alpha end fraction equals 10 over 8 end cell row cell cot space straight alpha end cell equals cell fraction numerator 1 over denominator tan space straight alpha end fraction equals 8 over 6 end cell end table end style 

0

Roboguru

Tentukan nilai dari keenam perbandingan trigonometri sudut  pada segitiga siku-siku berikut.

Pembahasan Soal:

Pertama kita cari sisi a

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row straight a equals cell square root of 25 squared minus 24 squared end root end cell row blank equals cell square root of 625 minus 576 end root end cell row blank equals cell square root of 49 end cell row blank equals 7 end table end style 

perbandingan trigonometri sudut begin mathsize 14px style straight alpha end style pada segitiga siku-siku

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell sin space straight alpha end cell equals cell de over mi equals 24 over 25 end cell row cell cos space straight alpha end cell equals cell sa over mi equals 7 over 25 end cell row cell tan space straight alpha end cell equals cell de over sa equals 24 over 7 end cell row cell cossec space straight alpha end cell equals cell fraction numerator 1 over denominator sin space straight alpha end fraction equals 25 over 24 end cell row cell sec space straight alpha end cell equals cell fraction numerator 1 over denominator cos space straight alpha end fraction equals 25 over 7 end cell row cell cot space straight alpha end cell equals cell fraction numerator 1 over denominator tan space straight alpha end fraction equals 7 over 24 end cell end table end style 

0

Roboguru

Tentukan nilai perbandingan trigonometri untuk  pada gambar berikut.

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight theta end cell equals cell depan over miring space end cell row blank equals cell 4 over 5 end cell row cell cos space straight theta end cell equals cell samping over miring end cell row blank equals cell 3 over 5 end cell row cell tan space straight theta end cell equals cell depan over samping end cell row blank equals cell 4 over 3 end cell row cell cosecan space straight theta end cell equals cell fraction numerator 1 over denominator sin space straight theta end fraction end cell row blank equals cell 5 over 4 end cell row cell secan space straight theta end cell equals cell fraction numerator 1 over denominator cos space straight theta end fraction end cell row blank equals cell 5 over 3 end cell row cell cotan space straight theta end cell equals cell fraction numerator 1 over denominator tan space straight theta end fraction end cell row blank equals cell 3 over 4 end cell end table 

0

Roboguru

Perhatikan segitiga di bawah ini! Tentukanlah: b. nilai , , , , ,

Pembahasan Soal:

Perhatikan perhitungan berikut ini.

Ingat:

Teorema Pythagoras.

begin mathsize 14px style c squared equals a squared plus b squared end style

Perbandingan sisi trigonometri pada segitiga.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight alpha end cell equals cell de over mi end cell row cell cos space straight alpha end cell equals cell sa over mi end cell row cell tan space straight alpha end cell equals cell de over sa end cell row cell cosec space straight alpha end cell equals cell fraction numerator 1 over denominator sin space straight alpha end fraction end cell row cell sec space straight alpha end cell equals cell fraction numerator 1 over denominator cos space straight alpha end fraction end cell row cell cotan space straight alpha end cell equals cell fraction numerator 1 over denominator tan space straight alpha end fraction end cell end table end style

Untuk mencari panjang begin mathsize 14px style KM end style dapat menggunakan teorema Pythagoras, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell KL squared end cell equals cell LM squared plus KM squared end cell row cell 15 squared end cell equals cell 12 squared plus KM squared end cell row 225 equals cell 144 plus KM squared end cell row cell 225 minus 144 end cell equals cell KM squared end cell row 81 equals cell KM squared end cell row cell plus-or-minus square root of 81 end cell equals KM row cell plus-or-minus 9 end cell equals KM end table end style

Didapatkan panjang undefined adalah begin mathsize 14px style plus-or-minus 9 end style, karena suatu panjang tidak mungkin negatif maka dipilih begin mathsize 14px style 9 end style. Jadi, panjang undefined adalah begin mathsize 14px style 9 space cm end style.

Sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight alpha end cell equals cell de over mi equals 12 over 15 equals 4 over 5 end cell row cell cos space straight alpha end cell equals cell sa over mi equals 9 over 15 equals 3 over 5 end cell row cell tan space straight alpha end cell equals cell de over sa equals 12 over 9 equals 4 over 3 end cell row cell cosec space straight alpha end cell equals cell fraction numerator 1 over denominator sin space straight alpha end fraction equals fraction numerator 1 over denominator begin display style 4 over 5 end style end fraction equals 5 over 4 end cell row cell sec space straight alpha end cell equals cell fraction numerator 1 over denominator cos space straight alpha end fraction equals fraction numerator 1 over denominator begin display style 3 over 5 end style end fraction equals 5 over 3 end cell row cell cotan space straight alpha end cell equals cell fraction numerator 1 over denominator tan space straight alpha end fraction equals fraction numerator 1 over denominator begin display style 4 over 3 end style end fraction equals 3 over 4 end cell end table end style

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