Geometry Problem Solving Drill – 13: Parallelograms Question No. 1
... Question 1. Mr. Smith’s garden has 4 equal sides. It has 2 pairs of parallel sides. There are no right angles. Choose the most precise name for the shape of Mr. Smith’s garden. ...
... Question 1. Mr. Smith’s garden has 4 equal sides. It has 2 pairs of parallel sides. There are no right angles. Choose the most precise name for the shape of Mr. Smith’s garden. ...
TRIGONOMETRIC FUNCTIONS Teacher`s Guide
... 5. Students may be interested in why we seem to always rotate in a counterclockwise direction. It should be explained that, from its initial position on the positive X-axis, the terminal arm may rotate in either direction. By convention, mathematicians have decided that, if the rotation is counterc ...
... 5. Students may be interested in why we seem to always rotate in a counterclockwise direction. It should be explained that, from its initial position on the positive X-axis, the terminal arm may rotate in either direction. By convention, mathematicians have decided that, if the rotation is counterc ...
Rectilinear Plane Figures 23 - e
... You learned in Grade 6 that a closed plane figure made up of three straight line segments is a triangle. Similary, we know that these line segment are the sides of the triangle and the points at which the sides meet are the vertices of the triangle. Activity 23.1 Study the following triangles, well. ...
... You learned in Grade 6 that a closed plane figure made up of three straight line segments is a triangle. Similary, we know that these line segment are the sides of the triangle and the points at which the sides meet are the vertices of the triangle. Activity 23.1 Study the following triangles, well. ...
Properties of Circles second point on the circle
... Using the original point on the circle, increase and decrease the size of the circle. What do you notice about the measurements you made? ii. Using the second point on the circle, move it around the circumference, changing the length of the chord. What do you notice about the measurements you made? ...
... Using the original point on the circle, increase and decrease the size of the circle. What do you notice about the measurements you made? ii. Using the second point on the circle, move it around the circumference, changing the length of the chord. What do you notice about the measurements you made? ...
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.