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Borda–Carnot equation is an empirical description of the mechanical energy losses of the fluid due to a (sudden) flow expansion. It describes how the total ... 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/
In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present ... more
In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability ... more
Earned value management (EVM), earned value project management, or earned value performance management (... more
An exact description of friction loss (Darcy Weisbach equation) for Bingham plastics in fully developed laminar pipe flow was first published by ... more
The arithmetic mean (or simply “mean”) of a sample x1,x2,.x3, ... xn is the sum of the sampled values divided by the number of items in the ... more
The Sérsic profile (or Sérsic model or Sérsic’s law) is a mathematical function that describes how the intensity I of a galaxy varies with distance ... more
A rocket engine nozzle is a propelling nozzle (usually of the de Laval type) used in a rocket engine to expand and accelerate the combustion gases produced ... more
Lotka’s law, named after Alfred J. Lotka, is one of a variety of special applications of Zipf’s law. It describes the frequency of publication ... 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.