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Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... more
Pressure vessels are held together against the gas pressure due to tensile forces within the walls of the container. The normal (tensile) stress in the ... more
Diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration ... more
An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... more
An electromagnet is a type of magnet in which the magnetic field is produced by electric current. The magnetic field disappears when the current is turned ... more
The Townsend discharge is a gas ionization process where free electrons, accelerated by a sufficiently strong electric field, give rise to electrical ... more
Electric potential energy, or electrostatic potential energy, is a potential energy that results from conservative Coulomb forces and is associated with ... 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/
Heat transfer describes the exchange of thermal energy, between physical systems depending on the temperature and pressure, by dissipating heat. The heat ... 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.