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Return over a single period

In finance, return is a profit on an investment. return is also used to refer to a profit on an investment, expressed as a proportion of the amount ... more

Bipolar junction transistor (Common-emmiter current gain )

A bipolar junction transistor (or bipolar transistor) is a type of transistor that relies on the contact of two types of semiconductor for its operation. ... more

Power AC (3-phases)

Three phases AC power produced from three sinusoidal voltages which are generated out of phase with each other

... more

Smeed's Law

Smeed’s Law, named after R. J. Smeed, who first proposed the relationship in 1949, is an empirical rule relating traffic fatalities to traffic ... more

Working Load Limit

Safe Working Load (SWL) sometimes stated as the Normal Working Load (NWL) is the maximum safe force ... more

Electromotive force - the charge

Electromotive force, abbreviated emf (denoted ℰ and measured in volts) is the electrical intensity or “pressure” developed by a source 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/
Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

Hyperbolic discounting

Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a ... more

Ohm's Law

Ohm’s law states that the current through a conductor between two points is directly proportional to the potential difference across the two points, ... more

NPN bipolar transistor (Ebers–Moll model)

A bipolar junction transistor (BJT or bipolar transistor) is a type of transistor that relies on the contact of two types of ... more

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