angle of depression
... horizontal line and a line of sight to a point above the line. In the diagram, 1 is the angle of elevation from the tower T to the plane P. An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line. 2 is the angle of depression from the plane to ...
... horizontal line and a line of sight to a point above the line. In the diagram, 1 is the angle of elevation from the tower T to the plane P. An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line. 2 is the angle of depression from the plane to ...
G-CO.C.10
... prove and apply the idea that the segment joining midpoints of two sides of a triangle are parallel to the third side and half the length. prove the medians of a triangle meet at the centroid. prove the perpendicular bisectors of a triangle meet at the circumcenter. prove the altitudes of a ...
... prove and apply the idea that the segment joining midpoints of two sides of a triangle are parallel to the third side and half the length. prove the medians of a triangle meet at the centroid. prove the perpendicular bisectors of a triangle meet at the circumcenter. prove the altitudes of a ...
Box 6. Kästner`s Argument for Anti
... involve a vertical motion as part of the other two motions. We’ll use an example with lines instead of surfaces, which makes the same point. For the straight line, you only need to go one direction, over. But for the curved line you need to go over, and then up. You can get everywhere on the straigh ...
... involve a vertical motion as part of the other two motions. We’ll use an example with lines instead of surfaces, which makes the same point. For the straight line, you only need to go one direction, over. But for the curved line you need to go over, and then up. You can get everywhere on the straigh ...
Lesson Warm Up 6 1. congruent angles 2. x = 45 3. collinear: B
... form another unique plane. 5. x = 26 6. Since an infinite number of planes can be drawn through a line, and the point is also on the line, the statement should be, “If a point is on a line, there are an infinite number of planes that contain this line and the point.” ...
... form another unique plane. 5. x = 26 6. Since an infinite number of planes can be drawn through a line, and the point is also on the line, the statement should be, “If a point is on a line, there are an infinite number of planes that contain this line and the point.” ...
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others. Euler angles are also used to describe the orientation of a frame of reference (typically, a coordinate system or basis) relative to another. They are typically denoted as α, β, γ, or φ, θ, ψ.Euler angles represent a sequence of three elemental rotations, i.e. rotations about the axes of a coordinate system. For instance, a first rotation about z by an angle α, a second rotation about x by an angle β, and a last rotation again about z, by an angle γ. These rotations start from a known standard orientation. In physics, this standard initial orientation is typically represented by a motionless (fixed, global, or world) coordinate system; in linear algebra, by a standard basis.Any orientation can be achieved by composing three elemental rotations. The elemental rotations can either occur about the axes of the fixed coordinate system (extrinsic rotations) or about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation (intrinsic rotations). The rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a local coordinate system. Without considering the possibility of using two different conventions for the definition of the rotation axes (intrinsic or extrinsic), there exist twelve possible sequences of rotation axes, divided in two groups: Proper Euler angles (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y) Tait–Bryan angles (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z). Tait–Bryan angles are also called Cardan angles; nautical angles; heading, elevation, and bank; or yaw, pitch, and roll. Sometimes, both kinds of sequences are called ""Euler angles"". In that case, the sequences of the first group are called proper or classic Euler angles.