Jika cot θ=125​, dengan θ sudut lancip, tentukan nilai dari sin θ sec θ!

Pertanyaan

Jika begin mathsize 14px style cot space italic theta equals 5 over 12 end style, dengan begin mathsize 14px style italic theta end style sudut lancip, tentukan nilai dari begin mathsize 14px style sin space italic theta space sec space italic theta end style!

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

diperoleh nilai dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank theta end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank theta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 12 over 5 end cell end table end style.

Pembahasan

Berdasarkan informasi pada soal dan definisi fungsi trigonometri diketahui: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cot space theta end cell equals cell 5 over 12 end cell row cell cot space theta end cell equals cell fraction numerator 1 over denominator tan space theta end fraction end cell row cell sec space theta end cell equals cell fraction numerator 1 over denominator cos space theta end fraction end cell end table end style 

Sehingga dapat ditentukan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space theta space sec space theta end cell equals cell sin space theta cross times fraction numerator 1 over denominator cos space theta end fraction end cell row blank equals cell fraction numerator sin space theta over denominator cos space theta end fraction end cell row blank equals cell tan space theta end cell row blank equals cell fraction numerator 1 over denominator cot space theta end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 5 over 12 end style end fraction end cell row blank equals cell 12 over 5 end cell end table end style 

Dengan demikian, diperoleh nilai dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank theta end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sec end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank theta end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 12 over 5 end cell end table end style.

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