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The beta angle is a measurement that is used most notably in spaceflight. The beta angle determines the percentage of time an object such as a spacecraft ... more
The theory of solar cells explains the process by which light energy in photons is converted into electric current when the photons strike a suitable ... more
Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more
To rotate the position of the character, we can imagine it as a point on a circle, and we will change the angle of the point by 20 degrees. To do so, we first need to find the radius of this circle and the original angle.
Drawing a right triangle inside the circle, we can find the radius using the Pythagorean Theorem:
To find the angle, we need to decide first if we are going to find the acute angle of the triangle, the reference angle, or if we are going to find the angle measured in standard position. While either approach will work, in this case we will do the latter. By applying the cosine function and using our given information we get
While there are two angles that have this cosine value, the angle of 120.964 degrees is in the second quadrant as desired, so it is the angle we were looking for.
Rotating the point clockwise by 20 degrees, the angle of the point will decrease to 100.964 degrees. We can then evaluate the coordinates of the rotated point
For x axis:
For y axis:
The coordinates of the character on the rotated map will be (-1.109, 5.725)
Reference : PreCalculus: An Investigation of Functions,Edition 1.4 © 2014 David Lippman and Melonie Rasmussen
http://www.opentextbookstore.com/precalc/
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/
A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. It has six edges and four ... more
Ceva’s theorem is a theorem about triangles in Euclidean plane geometry. Given a triangle ABC, let the lines AO, BO and CO ... more
Menelaus’ theorem, named for Menelaus of Alexandria, is a theorem about triangles in plane geometry. Given a triangle ABC, ... more
Flux is two separate simple and ubiquitous concepts throughout physics and applied mathematics. Within a discipline, the term is generally used ... more
The volumetric flow rate is the volume of fluid which passes through a given surface per unit time. Fow velocity in fluid dynamics or drift velocity in ... more
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In a video game design, a map shows the location of other characters relative to the player, who is situated at the origin, and the direction they are facing. A character currently shows on the map at coordinates (-3, 5). If the player rotates counterclockwise by 20 degrees, then the objects in the map will correspondingly rotate 20 degrees clockwise. Find the new coordinates of the character.