Trigonometric Values of Special Angles

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s i n α = \frac{a}{c}, c o s α = \frac{b}{c}, t g α = \frac{a}{b}, c t g α = \frac{b}{a}

α = 0 ° = 2 π

$\sin 0 °$	$\cos 0 °$	$tg 0 °$	$ctg 0 °$
$0$	$1$	$0$	$+∞$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 30 ° = \frac{π}{6}

Trigonometric Values of Special Angles

$\sin 30 °$	$\cos 30 °$	$tg 30 °$	$ctg 30 °$
$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{3}}{3}$	$\sqrt{3}$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 45 ° = \frac{π}{4}

Trigonometric Values of Special Angles

$\sin 45 °$	$\cos 45 °$	$tg 45 °$	$ctg 45 °$
$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$1$	$1$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 60 ° = \frac{π}{3}

Trigonometric Values of Special Angles

$\sin 60 °$	$\cos 60 °$	$tg 60 °$	$ctg 60 °$
$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$	$\frac{\sqrt{3}}{3}$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 90 ° = \frac{π}{2}

Trigonometric Values of Special Angles

$\sin 90 °$	$\cos 90 °$	$tg 90 °$	$ctg 90 °$
$1$	$0$	$+ \infty$	$0$

α = 120 ° = \frac{2π}{3}

Trigonometric Values of Special Angles

$\sin 120 °$	$\cos 120 °$	$tg 120 °$	$ctg 120 °$
$\frac{\sqrt{3}}{2}$	$- \frac{1}{2}$	$- \sqrt{3}$	$- \frac{\sqrt{3}}{3}$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 135 ° = \frac{3π}{4}

Trigonometric Values of Special Angles

$\sin 135 °$	$\cos 135 °$	$tg 135 °$	$ctg 135 °$
$\frac{\sqrt{2}}{2}$	$- \frac{\sqrt{2}}{2}$	$- 1$	$- 1$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 150 ° = \frac{5π}{6}

Trigonometric Values of Special Angles

$\sin 150 °$	$\cos 150 °$	$tg 150 °$	$ctg 150 °$
$\frac{1}{2}$	$- \frac{\sqrt{3}}{2}$	$- \frac{\sqrt{3}}{3}$	$- \sqrt{3}$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 180 ° = π

Trigonometric Values of Special Angles

$\sin 180 °$	$\cos 180 °$	$tg 180 °$	$ctg 180 °$
$0$	$- 1$	$0$	$- \infty$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 210 ° = \frac{7 π}{6}

Trigonometric Values of Special Angles

$\sin 210 °$	$\cos 210 °$	$tg 210 °$	$ctg 210 °$
$- \frac{1}{2}$	$- \frac{\sqrt{3}}{2}$	$\frac{\sqrt{3}}{3}$	$\sqrt{3}$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 225 ° = \frac{5 π}{4}

Trigonometric Values of Special Angles

$\sin 225 °$	$\cos 225 °$	$tg 225 °$	$ctg 225 °$
$- \frac{\sqrt{2}}{2}$	$- \frac{\sqrt{2}}{2}$	$1$	$1$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 240 ° = \frac{4 π}{3}

Trigonometric Values of Special Angles

$\sin 240 °$	$\cos 240 °$	$tg 240 °$	$ctg 240 °$
$- \frac{\sqrt{3}}{2}$	$- \frac{1}{2}$	$\sqrt{3}$	$\frac{\sqrt{3}}{3}$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 270 ° = \frac{3 π}{6}

Trigonometric Values of Special Angles

$\sin 270 °$	$\cos 270 °$	$tg 270 °$	$ctg 270 °$
$- 1$	$0$	$- \infty$	$0$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 300 ° = \frac{5π}{3}

Trigonometric Values of Special Angles

$\sin 300 °$	$\cos 300 °$	$tg 300 °$	$ctg 300 °$
$- \frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$- \sqrt{3}$	$- \frac{\sqrt{3}}{3}$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 315 ° = \frac{7 π}{4}

Trigonometric Values of Special Angles

$\sin 315 °$	$\cos 315 °$	$tg 315 °$	$ctg 315 °$
$- \frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$- 1$	$- 1$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

α = 330 ° = \frac{11 π}{6}

Trigonometric Values of Special Angles

$\sin 330 °$	$\cos 330 °$	$tg 330 °$	$ctg 330 °$
$- \frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$- \frac{\sqrt{3}}{3}$	$- \sqrt{3}$

0° 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

Keywords: Trigonometric Values of Special Angles

Trigonometry
Law of Sines
Law of Cosines
Trigonometric identities of double angles
Trygonometry Identities of same angle
Trigonometric identities of half angles
Identities for the sum and difference of two angles
Sum and difference of trigonometric functions
Trigonometric Values of Special Angles
Two-dimensional geometric shapes
Angle Bisector Theorem
Basic Proportionality Theorem - Intercept Theorem
The inscribed angle theorem
Convex - Concave polygons, functions
Triangle
Special Triangles - Right Triangle, Equilateral Triangles, Isosceles Triangles
Quadrilateral
Squere
Rectangle
Rhombus
Parallelogram
Kite
Trapezoid
Circle
Circular sector
Circular segment
Three-dimensional geometric shapes
Cube
Sphere
Cone
Prism
Pyramide
Platonic solids
Cylinder
Vectors
Scalar Product of Vectors
Vector Product of Vectors
Analytical Geometry 2D
Distance between two points
Circle
Linear equation
Ellipse
Analytical Geometry 3D
Plane