Pertanyaan

Tentukan nilai dari: a. sin 6 0 ∘ cotg 6 0 ∘ + sec 4 5 ∘ cos 45

Tentukan nilai dari:

a. $sin 6 0^{\circ} cotg 6 0^{\circ} + sec 4 5^{\circ} cos 45$

F. Faiz

Master Teacher

Jawaban terverifikasi

Pembahasan

Ingatlah pada perbandingan sisi (trigonometri), yaitu: Sehingga diperoleh nilai sudut trigonometri yaitu: Maka, nilai dari adalah .

Ingatlah pada perbandingan sisi (trigonometri), yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell sec space straight alpha end cell equals cell fraction numerator 1 over denominator cos space straight alpha end fraction end cell row cell cotg space straight alpha end cell equals cell fraction numerator 1 over denominator tan space straight alpha end fraction end cell end table$

Sehingga diperoleh nilai sudut trigonometri yaitu:

$sin space 60 degree space cotg space 60 degree plus sec space 45 degree space cos space 45 equals sin space 60 degree times fraction numerator 1 over denominator tan space 60 degree end fraction plus fraction numerator 1 over denominator cos space 45 degree end fraction times cos space 45 degree equals 1 half down diagonal strike square root of 3 end strike times fraction numerator 1 over denominator down diagonal strike square root of 3 end strike end fraction plus fraction numerator 1 over denominator down diagonal strike begin display style 1 half end style square root of 2 end strike end fraction times down diagonal strike 1 half square root of 2 end strike equals 1 half plus 1 equals 1 half plus 2 over 2 equals 3 over 2$

Maka, nilai dari sin space 60 degree space cotg space 60 degree plus sec space 45 degree space cos space 45 adalah 3 over 2 .