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Péclet number (for heat transfer)

The Péclet number (Pe) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is named after the French ... more

Avogadro's law

Avogadro’s law is an experimental gas law relating volume of a gas to the amount of substance of gas present. Avogadro’s law states that, ... more

Specific gas constant (related to heat capacities)

The specific gas constant of a gas or a mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas/mixture. ... more

Tractive Force

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Mole fraction

In chemistry, the mole fraction is defined as the amount of a constituent divided by the total amount of all constituents in a mixture.The mole fraction ... more

Hawking Radiation - Temperature of a black body (or a black hole)

A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A black hole ... more

Worksheet 334

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.

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:

Pythagorean theorem (right triangle)

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

Cosine function

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:

Cosine function

For y axis:

Sine function

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
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

Miles Equation

In 1954, Miles developed his version of this equation for GRMS as he was researching fatigue failure of aircraft structural ... more

Hydrostatic weighing

Hydrostatic weighing, also referred to as “underwater weighing,” “hydrostatic body composition analysis,” and ... more

Radiation Pressure by Reflection (using particle model: photons)

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. Radiation pressure implies an interaction between ... more

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