sin(4pi/3)=-1/2 The sine of 4pi/3 is -1/2. Sin and cosine are trigonometric functions. Sin is the function that returns the ratio of the side opposite of an angle to the hypotenuse, while cosine is the function that returns the ratio of the side adjacent to an angle to the hypotenuse. In other words, sin(x) = opp/hyp and cos(x) = adj/hyp. These ratios can be used to find missing sides and angles in a triangle.

Trigonometry is the branch of mathematics that deals with the relations between the sides and angles of triangles. Trigonometry is used to calculate unknown angles and sides in a triangle when certain other angles and sides are known. It is also used in navigation, surveying, engineering, and physics.

In geometry, a hypotenuse is the longest side of a right angled triangle. The other two sides are known as the catheti. The length of the hypotenuse can be found using the Pythagorean theorem, which states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem is represented by the equation: hyp^2 = cat1^2 + cat2^2.

For example, in a right angled triangle with sides 3 and 4, the length of the hypotenuse would be 5 (because 3^2 + 4^2 = 9 + 16 = 25 = 5^2).