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The aspect ratio of an image describes the proportional relationship between its width and its height. The most common aspect ratios used today in the ... more
Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. ... more
The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes x, y, and z, it ... more
A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a completely round ball. A sphere is ... more
Wheel flop refers to steering behavior in which a bicycle or motorcycle tends to turn more than expected due to the front wheel “flopping” over ... more
Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average, or equilibrium) atmospheric pressure, caused by a sound ... 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/
Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, ... more
Octagon is a polygon that has eight sides.
A regular octagon is a closed figure with sides of the same length and internal angles of the same size.
... more
Noise figure (NF) and noise factor (F) are measures of degradation of the signal-to-noise ratio (SNR), caused by components in 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.