Lesson Title:Reading Graphs for Information
... Gr. 6 – classify and construct polygons and angles Reasoning and Proving – develop and apply reasoning skills to make and investigate conjectures and construct and defend arguments Representing – develop and apply reasoning skills to make and investigate conjectures and construct and defend argument ...
... Gr. 6 – classify and construct polygons and angles Reasoning and Proving – develop and apply reasoning skills to make and investigate conjectures and construct and defend arguments Representing – develop and apply reasoning skills to make and investigate conjectures and construct and defend argument ...
Andrew Ryba Math Intel Research Final Paper 6/7/09 (revision 6/17
... radii to the distance between the centers of the incircle and circumcircle. We do not know for certain if such a formula even exists. We know that a quadrilateral is cyclic if and only if its opposite angles are supplementary. The condition for a quadrilateral to have an inscribed circle is not so w ...
... radii to the distance between the centers of the incircle and circumcircle. We do not know for certain if such a formula even exists. We know that a quadrilateral is cyclic if and only if its opposite angles are supplementary. The condition for a quadrilateral to have an inscribed circle is not so w ...
1.2 Exercises
... rotation, celestial objects like the moon and the stars appear to move across the sky, rising in the east and setting in the west. As a result, if a telescope on Earth remains stationary while viewing a celestial object, the object will slowly move outside the viewing field of the telescope. For thi ...
... rotation, celestial objects like the moon and the stars appear to move across the sky, rising in the east and setting in the west. As a result, if a telescope on Earth remains stationary while viewing a celestial object, the object will slowly move outside the viewing field of the telescope. For thi ...
Study Guide and Intervention (continued) /
... An altitude to the hypotenuse of a right triangle forms two right triangles. The two triangles are similar and each is similar to the original triangle. ...
... An altitude to the hypotenuse of a right triangle forms two right triangles. The two triangles are similar and each is similar to the original triangle. ...
Activities
... Provide students with centimetre grid paper and triangular or isometric grid paper (use BLM 7 and 8 on pages 2 and 3). 1. Have students draw two congruent regular polygons in different orientations on square dot paper or triangular dot paper. Ask them to compare the lengths of the sides of the polyg ...
... Provide students with centimetre grid paper and triangular or isometric grid paper (use BLM 7 and 8 on pages 2 and 3). 1. Have students draw two congruent regular polygons in different orientations on square dot paper or triangular dot paper. Ask them to compare the lengths of the sides of the polyg ...
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.