Selesaikan sin((pidiv12)

$$\sin ( ( \pi \div 12 )$$

Evaluasi

$$\frac{\sqrt{6}-\sqrt{2}}{4}\approx 0,258819045$$

Langkah Solusi

Gunakan \sin(x-y)=\sin(x)\cos(y)-\sin(y)\cos(x) di mana x=\frac{\pi }{4} dan y=\frac{\pi }{6} untuk mendapatkan hasilnya.

$$\sin(\frac{\pi }{4}-\frac{\pi }{6})=\sin(\frac{\pi }{4})\cos(\frac{\pi }{6})-\sin(\frac{\pi }{6})\cos(\frac{\pi }{4})$$

Dapatkan nilai \sin(\frac{\pi }{4}) dari tabel nilai trigonometri.

$$\frac{\sqrt{2}}{2}\cos(\frac{\pi }{6})-\sin(\frac{\pi }{6})\cos(\frac{\pi }{4})$$

Dapatkan nilai \cos(\frac{\pi }{6}) dari tabel nilai trigonometri.

$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}-\sin(\frac{\pi }{6})\cos(\frac{\pi }{4})$$

Dapatkan nilai \sin(\frac{\pi }{6}) dari tabel nilai trigonometri.

$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}-\frac{1}{2}\cos(\frac{\pi }{4})$$

Dapatkan nilai \cos(\frac{\pi }{4}) dari tabel nilai trigonometri.

$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}}{2}-\frac{1}{2}\times \frac{\sqrt{2}}{2}$$

Lakukan penghitungan.

$$\frac{\sqrt{6}-\sqrt{2}}{4}$$