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A circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is called ... 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 celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. ... more
In crystallography, the triclinic crystal system is one of the 7 crystal systems. A crystal system is described by three basis vectors. In the triclinic ... more
A seiche (/ˈseɪʃ/ SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related ... more
In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or ... more
Hyperbola is the set of all points in the plane, such that the absolute value of the difference of each of the distances from two fixed points is constant. ... more
In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While mathematical ... more
Marconi’s law is the relation between height of antennas and maximum signaling distance of radio transmissions. Guglielmo Marconi enunciated at one ... more
A pendulum is a mass that is attached to a pivot, from which it can swing freely. Pendulum consisting of an actual object allowed to rotate freely around a ... 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.