Sec_7.1
... Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30, 45, 60, 120 , etc.). So, you will still need those unit circle values. We’ll use right triangle trigonometry to find the lengths of a ...
... Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30, 45, 60, 120 , etc.). So, you will still need those unit circle values. We’ll use right triangle trigonometry to find the lengths of a ...
Notes - 8.2 (4e)
... ASA = Angle, the Side between them, and another Angle SAA = Side, an Angle on one end, and the remaining Angle that doesn't touch the Side If we're working with this case, then we're good to go – plug and chug, and everything will turn out fine. This is because with two angles, and one side, we can ...
... ASA = Angle, the Side between them, and another Angle SAA = Side, an Angle on one end, and the remaining Angle that doesn't touch the Side If we're working with this case, then we're good to go – plug and chug, and everything will turn out fine. This is because with two angles, and one side, we can ...
Key
... 40. A plane that appears to be parallel to plane ABC: ____________ Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 41. 6 and 10 are __________________________ angles. 42. 7 and 9 are _________________ ...
... 40. A plane that appears to be parallel to plane ABC: ____________ Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 41. 6 and 10 are __________________________ angles. 42. 7 and 9 are _________________ ...
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.