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Vickers hardness number

The Vickers hardness test was developed in 1921 by Robert L. Smith and George E. Sandland at Vickers Ltd as an alternative to the Brinell method to measure ... more

Angular velocity

In physics, the angular velocity is defined as the rate of change of angular displacement and is a vector quantity (more precisely, a pseudovector) which ... more

Relation between permeability and magnetic susceptibility

Permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of ... more

Chebychev–Grübler–Kutzbach criterion

The Chebychev–Grübler–Kutzbach criterion determines the degree of freedom of a kinematic chain, that is, a coupling of rigid bodies by means of mechanical ... more

Auger electron spectroscopy - Electron impact cross-section (account for matrix effects)

Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... more

Planck temperature

Planck temperature, denoted by TP, is the unit of temperature in the system of natural units known as Planck units.

It serves as the ... more

Coefficient A(T,P) - used in UNESCO equation

The coefficient A(T,P) used in the UNESCO equation, speed of sound in sea water), depends on the temperature and the pressure

... more

Coefficient Cw(T,P) - used in UNESCO equation

The coefficient Cw (used in the UNESCO equation, speed of sound in sea water), depends on the temperature and the pressure

... 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/

Planet Formation Equation - "Clearing the neighbourhood"

“Clearing the neighbourhood around its orbit” is a criterion for a celestial body to be considered a planet in the Solar System. This was one ... more

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