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Nernst Equation - electrochemical half cell

In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell ... more

Coupled inductors

The voltage of one of the two nearby coupled inductors

... more

Compound pendulum (momemt of inertia)

A compound pendulum is a body formed from an assembly of particles or continuous shapes that rotates rigidly around a pivot. Its moments of inertia is the ... more

Rule of 70 ( estimating the time for money's buying power to halve)

Purchasing power (sometimes retroactively called adjusted for inflation) is the number of goods or services that can be purchased with a unit of currency. ... 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/
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

Implied repo rate

A repurchase agreement, also known as a repo, RP, or sale and repurchase agreement, is the sale of securities together with an agreement for the seller to ... more

Front focal length (FFL)

A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of ... more

Speeds and feeds - feed rate

The phrase speeds and feeds or feeds and speeds refers to two separate velocities in machine tool practice, cutting speed and feed rate. They are often ... more

Van 't Hoff equation

The Van 't Hoff equation in chemical thermodynamics relates the change in the equilibrium constant, Keq, of a chemical equilibrium to the change in ... more

Area thermal expansion coefficient

Thermal expansion is the tendency of matter to change in length, area or volume in response to a change in temperature, through heat transfer.
The ... more

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