- Orthogonal projection of a point P on a straight line r: point of intersection of r with the straight line through P perpendicular to r.
- Directed line: a line on which one direction is described as positive and the other as negative.
- Coordinate system: pair of directed lines, called x-axis and y-axis, having a common point O (origin). Usually the axes are perpendicular and with the same unit of measurement; also you can rotate the x-axis until it overlaps with the y-axis with an anticlockwise rotation less than 180°. Normally the positive direction is from left to right for the x-axis and from the bottom to the top for the y-axis.
- X-coordinate of a point P: a number whose absolute value is the distance of P from the y-axis, and whose sign is positive or negative depending on whether P is to the right or to the left of the y-axis.
- Y-coordinate of a point P: a number whose absolute value is the distance of P from the x-axis, and whose sign is positive or negative depending on whether P is higher or lower of the y-axis.
- Half-line: each of the two parts into which a line is divided by his point P, called initial point.
- Positive x-semiaxis: half-line formed by the x-axis points that have positive or zero x-coordinate.
- Absolute angle: part of a plane, limited by two half-lines (called sides of the angle) that have the same initial point V. V is called the vertex of the angle.
- Measure of an angle in radians: ratio of the arc cut by the angle on a circumference with center at its vertex and the radius of the circle itself.
- Directed angle: angle generated by the rotation of an half-line around its origin; it is conventionally considered positive if the rotation is counterclockwise, negative otherwise. The starting and ending half-lines are denoted initial and terminal side of the angle.
- Standard position of a directed angle: by definition of sinα, cosα, the initial side must be the positive x-semiaxis, and then the vertex of the angle must be the origin of the coordinate system.
- sinα (read: sine of alfa): y-coordinate of the intersection point of the terminal side of the directed angle α and a circumference with center in the origin and radius equal to the unit of measurement; α is said argument of sine.
- cosα (read: cosine of alfa): x-coordinate of the intersection point of the terminal side of the directed angle α and a circumference with center in the origin and radius equal to the unit of measurement; α is said argument of cosine.
- first Prosthaphaeresis formula: sinp+sinq=2sin[(p+q)/2]cos[p-q)/2] (convert the sum of two sines into a product).
(read: nth root of x): number that, raised to the nth power (ie, multiplied by itself n times) gives x. If there are two solutions only the positive is accepted; n and x are called the index and radicand.
| Index | Next | Return to my compositions |