Trigonometric Identities and Specific Angle Values

sin(0°)

$$0$$

cos(0°)

$$1$$

sin(90°)

$$1$$

cos(90°)

$$0$$

sin(180°)

$$0$$

cos(180°)

$$-1$$

sin(270°)

$$-1$$

cos(270°)

$$0$$

sin(360°)

$$0$$

sin(15°) (π/12)

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

cos(15°) (π/12)

$\frac{\sqrt{3} + 1}{2\sqrt{2}}$"

tan(15°) (π/12)

$$2 - \sqrt{3}$$

sin(18°) (π/10)

$$\frac{\sqrt{5} - 1}{4}$$

cos(18°) (π/10)

$$\frac{\sqrt{10 + 2\sqrt{5}}}{4}$$

sin(36°) (π/5)

$$\frac{\sqrt{10 - 2\sqrt{5}}}{4}$$

cos(36°) (π/5)

$$\frac{\sqrt{5} + 1}{4}$$

sin(54°) (3π/10)

$$\frac{\sqrt{5} + 1}{4}$$

cos(54°) (3π/10)

$$\frac{\sqrt{10 - 2\sqrt{5}}}{4}$$

sin(72°) (2π/5)

$$\frac{\sqrt{10 + 2\sqrt{5}}}{4}$$

cos(72°) (2π/5)

$$\frac{\sqrt{5} - 1}{4}$$

Variation 1 (Power Reduction)

$$1 + \cos(2\theta) = 2\cos^{2}(\theta)$$

Variation 2 (Power Reduction)

$$1 - \cos(2\theta) = 2\sin^{2}(\theta)$$

Variation 3 (Power Reduction)

$$(\sin(\theta) + \cos(\theta))^{2} = 1 + \sin(2\theta)$$

Variation 4 (Power Reduction)

$$(