Koordinat Polar

  Titik \(\text{P(4, 4)}\) dapat diubah menjadi koordinat polar \((r, \alpha)\) \(r = \sqrt{4^2 + 4^2} = \sqrt{2\cdot 4^2} = 4\sqrt{2}\) \(\tan \alpha = \dfrac{4}{4} = 1\) \(\alpha = 45^{\circ}\dotso\dotso \text{ titik (4, 4) di kuadran I}\) Jadi \(\text{P(4, 4)} = \text{P}(4\sqrt{2}, 45^{\circ})\)     CONTOH SOAL     Soal 1 Tentukan koordinat polar dari […]

Sudut Negatif

\(\color{blue} \sin (-\alpha) = -\sin \alpha\) \(\color{blue} \cos (-\alpha) = \cos \alpha\) \(\color{blue} \tan (-\alpha) = -\tan \alpha\)   \(\color{blue} \csc (-\alpha) = -\csc \alpha\) \(\color{blue} \sec (-\alpha) = \sec \alpha\) \(\color{blue} \cot (-\alpha) = -\cot \alpha\)   CONTOH SOAL   Soal 1 Tentukan nilai \(\sin (-240^{\circ})\)   Soal 2 Tentukan nilai \(\cos (-315^{\circ})\)   […]

Sudut Besar

Diketahui \(\theta\) adalah suatu sudut yang lebih besar dari \(360^{\circ}\) dan \(\alpha\) adalah suatu sudut yang kurang dari \(360^{\circ}\) \(\color{blue}\sin \theta = \sin (n\cdot 360^{\circ} + \alpha) = \sin \alpha\) \(\color{blue}\cos \theta = \cos (n\cdot 360^{\circ} + \alpha) = \cos \alpha\) \(\color{blue}\tan \theta = \tan (n\cdot 360^{\circ} + \alpha) = \tan \alpha\) \(n\) = bilangan […]

Sudut Berelasi

Sebelum kita belajar tentang relasi sudut dalam trigonometri, kita pahami terlebih dahulu tentang letak kuadran yang berpengaruh pada nilai fungsi trigonometri   Letak Kuadran   Keterangan: Pada kuadran I \([0^{\circ} – 90^{\circ}]\) semua fungsi trigonometri bernilai positif Pada kuadran II \([90^{\circ} – 180^{\circ}]\) fungsi sinus dan juga cosecan bernilai positif, fungsi trigonometri yang lainnya bernilai […]

Sudut Istimewa

Sudut Istimewa $$0^{\circ}$$ $$30^{\circ}$$ $$45^{\circ}$$ $$60^{\circ}$$ $$90^{\circ}$$ sin $$0$$ $$\dfrac{1}{2}$$ $$\dfrac{1}{2}\sqrt{2}$$ $$\dfrac{1}{2}\sqrt{3}$$ $$1$$ cos $$1$$ $$\dfrac{1}{2}\sqrt{3}$$ $$\dfrac{1}{2}\sqrt{2}$$ $$\dfrac{1}{2}$$ $$0$$ tan $$0$$ $$\dfrac{1}{3}\sqrt{3}$$ $$1$$ $$\sqrt{3}$$ $$\infty$$ csc $$\infty$$ $$2$$ $$\sqrt{2}$$ $$\dfrac{2}{3}\sqrt{3}$$ $$1$$ sec $$1$$ $$\dfrac{2}{3}\sqrt{3}$$ $$\sqrt{2}$$ $$2$$ $$\infty$$ cot $$\infty$$ $$\sqrt{3}$$ $$1$$ $$\dfrac{1}{3}\sqrt{3}$$ $$0$$ Contoh Soal   Contoh 1 Tentukan nilai dari \(\dfrac{\sin 45^{\circ}\cdot \cos 30^{\circ} […]

Perbandingan Trigonometri

Perbandingan Trigonometri $$\sin \alpha = \dfrac{\text{depan}}{\text{miring}}$$ $$\csc \alpha = \dfrac{\text{miring}}{\text{depan}}$$ $$\cos \alpha = \dfrac{\text{samping}}{\text{miring}}$$ $$\sec\alpha = \dfrac{\text{miring}}{\text{samping}}$$ $$\tan \alpha = \dfrac{\text{depan}}{\text{samping}}$$ $$\cot \alpha = \dfrac{\text{samping}}{\text{depan}}$$ Sudut Istimewa $$0^{\circ}$$ $$30^{\circ}$$ $$45^{\circ}$$ $$60^{\circ}$$ $$90^{\circ}$$ sin $$0$$ $$\dfrac{1}{2}$$ $$\dfrac{1}{2}\sqrt{2}$$ $$\dfrac{1}{2}\sqrt{3}$$ $$1$$ cos $$1$$ $$\dfrac{1}{2}\sqrt{3}$$ $$\dfrac{1}{2}\sqrt{2}$$ $$\dfrac{1}{2}$$ $$0$$ tan $$0$$ $$\dfrac{1}{3}\sqrt{3}$$ $$1$$ $$\sqrt{3}$$ $$\infty$$ csc $$\infty$$ $$2$$ $$\sqrt{2}$$ $$\dfrac{2}{3}\sqrt{3}$$ […]