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Gas-discharge tubes (electrical oscillation's frequency)

In cold cathode tubes, the electric discharge in gas has three regions, with distinct current-voltage characteristics: a)Townsend discharge, below the ... more

Torsion

In solid mechanics, torsion is the twisting of an object due to an applied torque. It is expressed in newton metres (N·m) or foot-pound force (ft·lbf). In ... more

Characteristic Length

In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a ... more

Chladni’s law, named after Ernst Chladni, relates the frequency of modes of vibration for flat circular surfaces with fixed center as a function of ... 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
Subtraction

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
http://www.opentextbookstore.com/precalc/

Radial Thermal Resistance in composite walls (conduction)

Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance ... more

Estimate at completion (EAC)

Earned value management (EVM), earned value project management, or earned value performance management (... more

Cost performance index (CPI)

Earned value management (EVM), earned value project management, or earned value performance management (... more

To-complete performance index BAC (TCPI-BAC)

Earned value management (EVM), earned value project management, or earned value performance management (... more

Second moment of area - I-Beam (W-section)

An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... more

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