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An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances.In an ideal ... 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 fluid mechanics, specific weight ( or unit weight ) represents the force exerted by gravity on a unit volume of a fluid. Specific weight can be used as ... more
A solenoid is a coil wound into a tightly packed helix. In physics, the term refers specifically to a long, thin loop of wire, often wrapped around a ... more
The thermal de Broglie wavelength is the average de Broglie wavelength of the gas particles in an ideal gas at the specified temperature. We can take the ... more
In physics, Henry’s law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. ... more
Sensible heat is heat exchanged by a body or thermodynamic system that changes the temperature, and some macroscopic variables of the body, but leaves ... more
Solar cell efficiency is the ratio of the electrical output of a solar cell to the incident energy in the form of sunlight. The energy conversion ... more
Specific impulse (usually abbreviated Isp) is a measure of the efficiency of rocket and jet engines. By definition, it is the impulse delivered per unit of ... more
Thermal energy is a term sometimes used to refer to the internal energy present in a system in a state of thermodynamic equilibrium by virtue of its ... 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.