Post-Lesson Quiz – Answer Key
... 1) How are similar triangles related to trigonometry? Since all right triangles have exactly one right angle, any two right triangles with one pair of congruent acute angles will be similar by the Angle-Angle Similarity Postulate. Therefore, any right triangle with a given acute angle will have exac ...
... 1) How are similar triangles related to trigonometry? Since all right triangles have exactly one right angle, any two right triangles with one pair of congruent acute angles will be similar by the Angle-Angle Similarity Postulate. Therefore, any right triangle with a given acute angle will have exac ...
Course Standards link
... Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation v ...
... Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation v ...
August-September 2010 Vol. 15 No. 2 61 On the Sum o
... This is the general equation for the range of a projectile without friction, notice that if yi 0 , (3) will become R ...
... This is the general equation for the range of a projectile without friction, notice that if yi 0 , (3) will become R ...
Tests - Digital Commons @ Trinity
... 2. Determine whether the following statements following Venn diagram. are true or false. If false, provide a counter example. If two angles are supplementary, then the sum of their measures is 180°. If the sum of the measures of two angles is not 180°, then the two angles are not supplementary. 3. I ...
... 2. Determine whether the following statements following Venn diagram. are true or false. If false, provide a counter example. If two angles are supplementary, then the sum of their measures is 180°. If the sum of the measures of two angles is not 180°, then the two angles are not supplementary. 3. I ...
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.