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The user may choose to replace the inclination angle by its complement, the elevation angle (or altitude angle), measured upward between the reference plane and the radial line—i.e., from the reference plane upward (towards to the positive z-axis) to the radial line. The depression angle is the negative of the elevation angle.
It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ , and azimuthal angle φ . The symbol ρ ( rho ) is often used instead of r . In geometry , a coordinate system is a system that uses one or more numbers , or coordinates , to uniquely determine the position of the points or ...
An angle equal to 1 / 4 turn (90° or π / 2 radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular. [12] An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle [11] ("obtuse" meaning "blunt").
Hipparchus. The concepts of angle and radius were already used by ancient peoples of the first millennium BC.The Greek astronomer and astrologer Hipparchus (190–120 BC) created a table of chord functions giving the length of the chord for each angle, and there are references to his using polar coordinates in establishing stellar positions. [2]
Here, p is the (positive) length of the line segment perpendicular to the line and delimited by the origin and the line, and is the (oriented) angle from the x-axis to this segment. It may be useful to express the equation in terms of the angle α = φ + π / 2 {\displaystyle \alpha =\varphi +\pi /2} between the x -axis and the line.
A rhumb line appears as a straight line on a Mercator projection map. [1] The name is derived from Old French or Spanish respectively: "rumb" or "rumbo", a line on the chart which intersects all meridians at the same angle. [1] On a plane surface this would be the shortest distance between two points.
Every point on the line has a real-number coordinate, and every real number represents some point on the line. There are two degrees of freedom in the choice of Cartesian coordinate system for a line, which can be specified by choosing two distinct points along the line and assigning them to two distinct real numbers (most
The three coordinates (ρ, φ, z) of a point P are defined as: The radial distance ρ is the Euclidean distance from the z-axis to the point P.; The azimuth φ is the angle between the reference direction on the chosen plane and the line from the origin to the projection of P on the plane.