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In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.
1.The orbit of a ... more
The cross-section of a welded butt joint, with the darkest gray representing the weld or fusion zone, the medium gray the heat affected zone, and the ... 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/
Hydrostatic weighing, also referred to as “underwater weighing,” “hydrostatic body composition analysis,” and ... more
Relates the length of a median and the sides of an arbitrary triangle
... more
The resistance to the flow of heat by the material of pipe wall can be expressed as a “heat transfer coefficient of the pipe wall”. However, ... more
A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may ... more
In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, ... more
Stewart’s theorem yields a relation between the length of the sides of the triangle and the length of a cevian of the triangle. A cevian is any line ... more
The formula provides a way to determine the volume-based concentration of any individual gaseous component.
Dalton’s law is not strictly ... 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.