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In probability theory and statistics, kurtosis is any measure of the “tailedness” of the probability distribution of a real-valued random ... more
Log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. The standard ... more
In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The parameterization with k ... 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 general, an exponential function is one of an exponential form , where the base is “b” and the exponent is “x”. In general, the ... more
Arithmetic mean is the sum of a collection of numbers divided by the number of numbers in the collection. The collection is often a set of results of an ... more
In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The parameterization with α ... more
The Earth Similarity Index, ESI or “easy scale” is a measure of how physically similar a planetary-mass object is to ... more
rigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more
Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... 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.