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NPSH characterize the potential for cavitation. The suction head coefficient is a dimensionless measure of ... more
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more
The Kelvin–Helmholtz mechanism is an astronomical process that occurs when the surface of a star or a planet cools. The cooling causes the pressure to ... more
The Earth Similarity Index, ESI or “easy scale” is a measure of how physically similar a planetary-mass object is to ... more
The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to ... more
In electromagnetics, an antenna’s power gain or simply gain is a key performance figure which combines the antenna’s directivity and electrical ... more
In electromagnetics, an antenna’s power gain or simply gain is a key performance figure which combines the antenna’s directivity and electrical ... more
In mechanics and physics, simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. It ... 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 celestial mechanics, apsidal precession is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical ... 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.