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Future value is the value of an asset or cash at a specified date in the future, based on the value of that asset in the present. Future value of an ... more
The selection of synthetic membranes for a targeted separation process is usually based on few requirements. Membranes have to provide enough mass transfer ... more
The pipe organ is a musical instrument commonly used in churches or cathedrals that produces sound by driving pressurized air (called wind) through pipes ... 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/
Optimum HDTV viewing distance is the distance that provides the viewer with the optimum immersive visual ... more
Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... more
Earned value management (EVM), earned value project management, or earned value performance management (... more
A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical ... more
A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical ... more
Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... 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.