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Stokes’s law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid’s ... more
The latus rectum is the chord parallel to the directrix and passing through the focus (or one of the two foci).The semi-latus rectum is half the latus ... more
An ellipsoid is a closed quadric surface that is a three dimensional analogue of an ellipse.a, b, c.are called the semi-principal axes.They correspond to ... more
An ellipsoid is a closed quadric surface that is a three dimensional analogue of an ellipse.a, b, c.are called the semi-principal axes.They correspond to ... more
An ellipsoid is a closed quadric surface that is a three dimensional analogue of an ellipse.a, b, c.are called the semi-principal axes.They correspond to ... more
A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more
In optics, Miller’s rule is an empirical rule which gives an estimate of the order of magnitude of the nonlinear coefficient.
More formally, ... 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/
Time of flight (TOF) describes a variety of methods that measure the time that it takes for an object, particle or acoustic, ... more
In finance, return is a profit on an investment. It comprises any change in value, and interest or dividends or other such cash flows which the investor ... 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.