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Tentukan nilai sinus, kosinus, dan tangen untuk sudut P dan R pada setiap segitiga siku-siku di bawah ini. Nyatakan jawaban anda dalam bentuk paling sederhana! b.

Tentukan nilai sinus, kosinus, dan tangen untuk sudut  pada setiap segitiga siku-siku di bawah ini. Nyatakan jawaban anda dalam bentuk paling sederhana!

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D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

Tentukan terlebih dahulu ukuran sisi tegak segitiga siku-siku dengan menggunakan teorema Pythagoras: Nilai sinus, kosinus, dan tangen untuk sudut . Nilai sinus, kosinus, dan tangen untuk sudut .

Tentukan terlebih dahulu ukuran sisi tegak segitiga siku-siku dengan menggunakan teorema Pythagoras:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell PQ squared end cell equals cell PR squared minus QR squared end cell row cell PQ squared end cell equals cell 11 squared minus 7 squared end cell row cell PQ squared end cell equals cell 121 minus 49 end cell row cell PQ squared end cell equals 72 row PQ equals cell square root of 72 end cell row PQ equals cell 6 square root of 2 end cell end table end style 

Nilai sinus, kosinus, dan tangen untuk sudut begin mathsize 14px style straight P end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell sin space straight P end cell equals cell fraction numerator Sisi space depan space sudut space straight P over denominator Sisi space miring space sudut space straight P end fraction end cell row cell sin space straight P end cell equals cell QR over PR end cell row cell sin space straight P end cell equals cell 7 over 11 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell cos space straight P end cell equals cell fraction numerator Sisi space samping space sudut space straight P over denominator Sisi space miring space sudut space straight P end fraction end cell row cell cos space straight P end cell equals cell PQ over PR end cell row cell cos space straight P end cell equals cell fraction numerator 6 square root of 2 over denominator 11 end fraction end cell row cell cos space straight P end cell equals cell 6 over 11 square root of 2 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell tan space straight P end cell equals cell fraction numerator Sisi space depan space sudut space straight P over denominator Sisi space samping space sudut space straight P end fraction end cell row cell tan space straight P end cell equals cell QR over PQ end cell row cell tan space straight P end cell equals cell fraction numerator 7 over denominator 6 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row cell tan space straight P end cell equals cell fraction numerator 7 over denominator 6 cross times 2 end fraction square root of 2 end cell row cell tan space straight P end cell equals cell 7 over 12 square root of 2 end cell end table end style  

Nilai sinus, kosinus, dan tangen untuk sudut begin mathsize 14px style straight R end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell sin space straight R end cell equals cell fraction numerator Sisi space depan space sudut space straight R over denominator Sisi space miring space sudut space straight R end fraction end cell row cell sin space straight R end cell equals cell PQ over PR end cell row cell sin space straight R end cell equals cell fraction numerator 6 square root of 2 over denominator 11 end fraction end cell row cell sin space straight R end cell equals cell 6 over 11 square root of 2 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell cos space straight R end cell equals cell fraction numerator Sisi space samping space sudut space straight R over denominator Sisi space miring space sudut space straight R end fraction end cell row cell cos space straight R end cell equals cell QR over PR end cell row cell cos space straight R end cell equals cell 7 over 11 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell tan space straight R end cell equals cell fraction numerator Sisi space depan space sudut space straight R over denominator Sisi space samping space sudut space straight R end fraction end cell row cell tan space straight R end cell equals cell PQ over QR end cell row cell tan space straight R end cell equals cell fraction numerator 6 square root of 2 over denominator 7 end fraction end cell row cell tan space straight R end cell equals cell 6 over 7 square root of 2 end cell end table end style 

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