hitunglah tanpaa menggunakan kalkulator ataupun tabel trigonometri tentukan sin 105

Trigonometri

sin 105
= sin (60+45)
= sin 60 cos 45 + sin 45 cos60
= 1/4 √6 + 1/4 √2
= 1/4 (√6 + √2)

Gunakan rumus:

[tex]\boxed{\boxed{\sin(A+B)=\sin A\cdot\cos B+\sin B\cdot\cos A}}[/tex]


[tex]$\begin{align}\sin105^{\circ}&=\sin(45^{\circ}+60^{\circ})\\&=\sin45^{\circ}\cdot\cos60^{\circ}+\sin60^{\circ}\cdot\cos45^{\circ}\\&=\frac12\sqrt2\cdot\frac12+\frac12\sqrt3\cdot\frac12\sqrt2\\&=\frac14\sqrt2+\frac14\sqrt6\\&=\boxed{\frac14\left(\sqrt2+\sqrt6\right)}\end[/tex]