trigonometry tables

Take an x-axis and an y-axis (orthonormal) and let O be the origin. A circle centered in O and with radius = 1 is known as trigonometric circle or unit circle.

If P is a point from the circle and A is the angle between PO and x axis then:

• the x-coordinate of P is called the cosine of A. We write cos(A) or cos A;
• the y-coordinate of P is called the sine of A. We write sin(A) or sin A;
• the number sin(A)/cos(A) is called the tangent of A. We write tan(A) or tan A;
• the number cos(A)/sin(A) is called the cotangent of A. We write cot(A) or cot A.

The sine function

sin : R -> R
All trigonometric functions are periodic. The period of sin is 2π${\displaystyle \pi }$.
The range of the function is [-1,1].

The cosine function

cos : R -> R
The period of sin is 2π${\displaystyle \pi }$.
The range of the function is [-1,1].

The tangent function

tan : R -> R
The range of the function is R. Now, the period is π${\displaystyle \pi }$ and the function is undefined at x = (π${\displaystyle \pi }$/2) + kπ${\displaystyle \pi }$, k=0,1,2,...
The graph of the tangent function on the interval 0 - π${\displaystyle \pi }$

Animated graph(open in a new window):
The graph of the tangent function on the interval 0 - 2π${\displaystyle \pi }$

The cotangent function

cot : R -> R
The range of the function is R. The period is π${\displaystyle \pi }$and that the function is undefined at x = kπ${\displaystyle \pi }$, k=0,1,2,...

The values of sin, cos, tan, cot at the angles of 0°, 30°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°

Ao${\displaystyle A^o}$	0o${\displaystyle 0^o}$	30o${\displaystyle {30}^o}$	45o${\displaystyle {45}^o}$	60o${\displaystyle {60}^o}$	90o${\displaystyle {90}^o}$	120o${\displaystyle {120}^o}$	135o${\displaystyle {135}^o}$	150o${\displaystyle {150}^o}$	180o${\displaystyle {180}^o}$	210o${\displaystyle {210}^o}$	225o${\displaystyle {225}^o}$	240o${\displaystyle {240}^o}$	270o${\displaystyle {270}^o}$	300o${\displaystyle {300}^o}$	315o${\displaystyle {315}^o}$	330o${\displaystyle {330}^o}$	360o${\displaystyle {360}^o}$
Arad${\displaystyle Arad}$	0${\displaystyle 0}$	π6${\displaystyle \frac{\pi }{6}}$	π4${\displaystyle \frac{\pi }{4}}$	π3${\displaystyle \frac{\pi }{3}}$	π2${\displaystyle \frac{\pi }{2}}$	2π3${\displaystyle \frac{2\pi }{3}}$	3π4${\displaystyle \frac{3\pi }{4}}$	5π6${\displaystyle \frac{5\pi }{6}}$	π${\displaystyle \pi }$	7π6${\displaystyle \frac{7\pi }{6}}$	5π4${\displaystyle \frac{5\pi }{4}}$	4π3${\displaystyle \frac{4\pi }{3}}$	3π2${\displaystyle \frac{3\pi }{2}}$	5π3${\displaystyle \frac{5\pi }{3}}$	7π4${\displaystyle \frac{7\pi }{4}}$	11π6${\displaystyle \frac{11\pi }{6}}$	2π${\displaystyle 2\pi }$
sinA${\displaystyle \sin A}$	0${\displaystyle 0}$	12${\displaystyle \frac{1}{2}}$	2–√2${\displaystyle \frac{\sqrt{2}}{2}}$	3–√2${\displaystyle \frac{\sqrt{3}}{2}}$	1${\displaystyle 1}$	3–√2${\displaystyle \frac{\sqrt{3}}{2}}$	2–√2${\displaystyle \frac{\sqrt{2}}{2}}$	12${\displaystyle \frac{1}{2}}$	0${\displaystyle 0}$	−12${\displaystyle -\frac{1}{2}}$	−2–√2${\displaystyle -\frac{\sqrt{2}}{2}}$	−3–√2${\displaystyle -\frac{\sqrt{3}}{2}}$	−1${\displaystyle -1}$	−3–√2${\displaystyle -\frac{\sqrt{3}}{2}}$	−2–√2${\displaystyle -\frac{\sqrt{2}}{2}}$	−12${\displaystyle -\frac{1}{2}}$	0${\displaystyle 0}$
cosA${\displaystyle \cos A}$	1${\displaystyle 1}$	3–√2${\displaystyle \frac{\sqrt{3}}{2}}$	2–√2${\displaystyle \frac{\sqrt{2}}{2}}$	12${\displaystyle \frac{1}{2}}$	0${\displaystyle 0}$	−12${\displaystyle -\frac{1}{2}}$	−2–√2${\displaystyle -\frac{\sqrt{2}}{2}}$	−3–√2${\displaystyle -\frac{\sqrt{3}}{2}}$	−1${\displaystyle -1}$	−3–√2${\displaystyle -\frac{\sqrt{3}}{2}}$	−2–√2${\displaystyle -\frac{\sqrt{2}}{2}}$	−12${\displaystyle -\frac{1}{2}}$	0${\displaystyle 0}$	12${\displaystyle \frac{1}{2}}$	2–√2${\displaystyle \frac{\sqrt{2}}{2}}$	3–√2${\displaystyle \frac{\sqrt{3}}{2}}$	1${\displaystyle 1}$
tanA${\displaystyle \tan A}$	0${\displaystyle 0}$	3–√3${\displaystyle \frac{\sqrt{3}}{3}}$	1${\displaystyle 1}$	3–√${\displaystyle \sqrt{3}}$	−${\displaystyle -}$	−3–√${\displaystyle -\sqrt{3}}$	−1${\displaystyle -1}$	−3–√3${\displaystyle -\frac{\sqrt{3}}{3}}$	0${\displaystyle 0}$	3–√3${\displaystyle \frac{\sqrt{3}}{3}}$	1${\displaystyle 1}$	3–√${\displaystyle \sqrt{3}}$	−${\displaystyle -}$	−3–√${\displaystyle -\sqrt{3}}$	−1${\displaystyle -1}$	−3–√3${\displaystyle -\frac{\sqrt{3}}{3}}$	0${\displaystyle 0}$
cotA${\displaystyle \cot A}$	−${\displaystyle -}$	3–√${\displaystyle \sqrt{3}}$	1${\displaystyle 1}$	3–√3${\displaystyle \frac{\sqrt{3}}{3}}$	0${\displaystyle 0}$	−3–√3${\displaystyle -\frac{\sqrt{3}}{3}}$	−1${\displaystyle -1}$	−3–√${\displaystyle -\sqrt{3}}$	−${\displaystyle -}$	3–√${\displaystyle \sqrt{3}}$	1${\displaystyle 1}$	3–√3${\displaystyle \frac{\sqrt{3}}{3}}$	0${\displaystyle 0}$	−3–√3${\displaystyle -\frac{\sqrt{3}}{3}}$	−1${\displaystyle -1}$	−3–√${\displaystyle -\sqrt{3}}$	−${\displaystyle -}$

The easiest way to remember the basic values of sin and cos at the angles of 0°, 30°, 60°, 90°:
sin([0, 30, 45, 60, 90]) = cos([90, 60, 45, 30, 0]) = sqrt([0, 1, 2, 3, 4]/4)