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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
Horizontal Curves are one of the two important transition elements in geometric design for highways (along with Vertical Curves). A horizontal curve ... more
A number of systems exist for the conversion of grades from other countries into German grades. One such system, used by most universities in ... more
Two circles of non-equal radius, both in the same plane, are said to be tangent to each other if they meet at only one point.
Two circles are
... more
Calibrated airspeed (CAS) is indicated airspeed corrected for instrument and position error.
When flying at sea level ... more
Many government agencies and industries (such as aerospace) require the use of a margin of safety (MoS or M.S.) to describe the ratio of the strength of ... more
In turbomachinery, the slip factor is a measure of the fluid slip in the impeller of a compressor or a turbine, mostly a centrifugal machine. Fluid slip is ... 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/
Many agencies and organizations (such as aerospace) define the margin of safety (MoS or M.S.) including the design factor, in other words, the margin of ... more
Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of ... 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.