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Acceleration, in physics, is the rate at which the velocity of an object changes over time. Mathematically, instantaneous acceleration—acceleration over an ... more
The Black–Scholes /ˌblæk ˈʃoʊlz/ or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. ... more
In queueing theory, a discipline within the mathematical theory of probability, Little’s result, theorem, lemma, law, or formula is a theorem by John ... more
In respiratory physiology, airway resistance is the resistance of the respiratory tract to airflow during inspiration and expiration . Specific airway ... more
Trip distribution (or destination choice or zonal interchange analysis) is the second component (after trip generation, but before mode choice and route ... 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/
Functional Residual Capacity (FRC) is the volume of air present in the lungs, specifically the parenchyma tissues, at the end of ... more
assigns a magnitude number to quantify the energy released by an earthquake. The Richter scale is a base-10 logarithmic scale, which defines magnitude as ... more
Thermionic emission is the thermally induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal ... 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.