Chapter 10CE PowerPoint
... 6) From a window, 29.6 meters above the ground, the angle of elevation of the top of a building is 42°, while the angle of depression to the foot of the building is 32°. Find the height of the building. ...
... 6) From a window, 29.6 meters above the ground, the angle of elevation of the top of a building is 42°, while the angle of depression to the foot of the building is 32°. Find the height of the building. ...
The Unit Organizer
... angels, then the lines are perpendicular If two lines are perpendicular, then they intersect to form four right angles If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. If a transversal is perpendicular to one of two parallel lines, then it is perpendicu ...
... angels, then the lines are perpendicular If two lines are perpendicular, then they intersect to form four right angles If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. If a transversal is perpendicular to one of two parallel lines, then it is perpendicu ...
Law of Sines - cavanaughmath
... In Example 3 there were two possibilities for angle B, and one of these was not compatible with the rest of the information. In general, if sin A < 1, we must check the angle and its supplement as possibilities, because any angle smaller than 180 can be in the triangle. To decide whether either pos ...
... In Example 3 there were two possibilities for angle B, and one of these was not compatible with the rest of the information. In general, if sin A < 1, we must check the angle and its supplement as possibilities, because any angle smaller than 180 can be in the triangle. To decide whether either pos ...
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.