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Energy–maneuverability theory is a model of aircraft performance. It was developed by Col. John Boyd, and is useful in describing an aircraft’s ... more
In compressible fluid dynamics, impact pressure (dynamic pressure) is the difference between total pressure (also known as pitot pressure or stagnation ... 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/
Resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is ... more
Youden’s J statistic (also called Youden’s index) is a single statistic that captures the performance of a diagnostic test. Its value ranges ... more
Hydrostatic weighing, also referred to as “underwater weighing,” “hydrostatic body composition analysis,” and ... more
Roll-off is the steepness of a transmission function with frequency, particularly in electrical network analysis, and most especially in connection with ... more
This entry marks fxSolver’s 2000th equation milestone and is a kind contribution by Reddit user ... more
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature through heat transfer. For a solid, we can ignore ... more
In geometry, a solid angle is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the ... 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.