Situation 43: Can You Circumscribe a Circle about this Polygon?
... through the points EFG (in general, through the 3 points that occur at the polygon’s interior angles that are not greater than 180 degrees – this is possible because a concave quadrilateral will have exactly one interior angle greater than 180 degrees, in this case it’s angle EHG). Suppose point H l ...
... through the points EFG (in general, through the 3 points that occur at the polygon’s interior angles that are not greater than 180 degrees – this is possible because a concave quadrilateral will have exactly one interior angle greater than 180 degrees, in this case it’s angle EHG). Suppose point H l ...
Final Review Sheet (Holt Text)(2013)
... 16) Name all pairs of vertical angles. 20) Name all pairs of alternate exterior angles. 17) Name all pairs of same side interior angles 21) Name all pairs of same side exterior angles. 18) Name all pairs of corresponding angles. 22) Name all angles that are supplementary to 1. 19) Name all pairs o ...
... 16) Name all pairs of vertical angles. 20) Name all pairs of alternate exterior angles. 17) Name all pairs of same side interior angles 21) Name all pairs of same side exterior angles. 18) Name all pairs of corresponding angles. 22) Name all angles that are supplementary to 1. 19) Name all pairs o ...
A Review of Four High-School Mathematics Programs
... that standard. Occasionally, however, it was necessary to review content outside these core units, specifically when a particular concept in the core unit required an understanding of fundamental concepts from other units. Core units from different programs that are relevant to a particular standard ...
... that standard. Occasionally, however, it was necessary to review content outside these core units, specifically when a particular concept in the core unit required an understanding of fundamental concepts from other units. Core units from different programs that are relevant to a particular standard ...
Tessellations-KJK
... How to use functions of transformational geometry to manipulate shapes How to identify interior & exterior angles Angle properties for straight lines, equilateral triangles and other polygons How to identify a 2D shape They are working with an Euclidean Plane ...
... How to use functions of transformational geometry to manipulate shapes How to identify interior & exterior angles Angle properties for straight lines, equilateral triangles and other polygons How to identify a 2D shape They are working with an Euclidean Plane ...
Document
... De Moivre's Theorem – Let r(cos F+isin F) be a complex number and n be any real number. Then [r(cos F+isin F]n = rn(cos nF+isin nF) What is this saying? The resulting r value will be r to the nth power and the resulting angle will be n times the original angle. ...
... De Moivre's Theorem – Let r(cos F+isin F) be a complex number and n be any real number. Then [r(cos F+isin F]n = rn(cos nF+isin nF) What is this saying? The resulting r value will be r to the nth power and the resulting angle will be n times the original angle. ...
Trigonometric functions
In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component). More precise definitions are detailed below. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles (often right triangles). In this use, trigonometric functions are used, for instance, in navigation, engineering, and physics. A common use in elementary physics is resolving a vector into Cartesian coordinates. The sine and cosine functions are also commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations through the year.In modern usage, there are six basic trigonometric functions, tabulated here with equations that relate them to one another. Especially with the last four, these relations are often taken as the definitions of those functions, but one can define them equally well geometrically, or by other means, and then derive these relations.