Quiz 6.1-6.3 Review #2
... V. Let be a “special” angle. Find the value of the trig functions. Derive the values by 1) drawing , 2) finding the reference angle, 3) complete & label the triangle, 4) use side lengths to determine the function values. Do not do this from memory or from a table. 10) 135 , Find sin , tan ...
... V. Let be a “special” angle. Find the value of the trig functions. Derive the values by 1) drawing , 2) finding the reference angle, 3) complete & label the triangle, 4) use side lengths to determine the function values. Do not do this from memory or from a table. 10) 135 , Find sin , tan ...
... Line segments in the same plane which do not intersect are parallel Sometimes (when the segments lie on parallel lines) If two lines are cut by a transversal, the rays bisecting a pair of alternate interior angles are parallel. Sometimes – if the two lines cut by the transversal are parallel The opp ...
Accelerated Math 2
... cut out nine right triangles. One right triangle should have an acute angle of 5°, the next should have an acute angle of 10°, and so forth, all the way up to 45°. As you make the triangles, you should construct the right angles and, whenever possible, construct the required acute angle. You can use ...
... cut out nine right triangles. One right triangle should have an acute angle of 5°, the next should have an acute angle of 10°, and so forth, all the way up to 45°. As you make the triangles, you should construct the right angles and, whenever possible, construct the required acute angle. You can use ...
4.1 Apply Triangle Sum Properties
... 4.2 Apply Congruence and Triangles Obj.: Identify congruent figures. Key Vocabulary • Congruent figures - In t w o congruent figures, all t h e parts o f o n e f ig u r e ar e congruent t o t h e corresponding parts o f t h e other f ig u r e. • Corresponding parts - In co n g r u en t p o lyg o n ...
... 4.2 Apply Congruence and Triangles Obj.: Identify congruent figures. Key Vocabulary • Congruent figures - In t w o congruent figures, all t h e parts o f o n e f ig u r e ar e congruent t o t h e corresponding parts o f t h e other f ig u r e. • Corresponding parts - In co n g r u en t p o lyg o n ...
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.