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Crest vertical curves are curves which, when viewed from the side, are convex upwards. This includes vertical curves at hill crests, but it also includes ... more
Harmonic Drive is the brand name of strain wave gear trademarked by the Harmonic Drive company, and invented in 1957 by C.W. Musser.
It is very ... more
In optics, the f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture) of an optical system is the ratio of the lens’s focal ... more
In biology or human geography, population growth is the increase in the number of individuals in a population.
The “population growth ... more
In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more
In geometry and complex analysis, a Möbius transformation of the plane is a rational function of one complex variable. A Möbius transformation can be ... more
The Magnetic Prandtl number is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) ... more
In electronics, a vacuum tube, an electron tube, or colloquially a tube (North America) or valve (British usage), is a device that controls electric ... 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/
The air-to-cloth ratio is the volumetric flow rate of air flowing through a dust collector’s inlet duct divided by the total cloth area in the ... 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.