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The current yield, interest yield, income yield, flat yield, market yield, mark to market yield or running yield is a financial term used in reference to ... more

Google AdSense is a program run by Google that allows publishers in the Google Network of content sites to serve automatic text, image, video, or ... more

Debt Service Coverage Ratio (DSCR)

The debt service coverage ratio (DSCR), also known as “debt coverage ratio” (DCR), is the ... more

Google AdSense is a program run by Google that allows publishers in the Google Network of content sites to serve automatic text, image, video, or ... more

Dividend discount model ( Gordon growth model)

The dividend discount model is a method of valuing a company’s stock price based on the theory that its stock is worth the sum of all of its future ... 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 Â© 2014 David Lippman and Melonie Rasmussen
http://www.opentextbookstore.com/precalc/

Landauer's Principle

Landauer’s principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that “any ... more

Declination of the Sun (simplified)

The position of the Sun in the sky is a function of both time and the geographic coordinates of the observer on the surface of the Earth. As the Earth ... more

Declination of the Sun

The position of the Sun in the sky is a function of both time and the geographic coordinates of the observer on the surface of the Earth. As the Earth ... more

Present value of an annuity due

An annuity is a series of payments made at fixed intervals of time. An annuity-due is an annuity whose payments are made at the beginning of each period. ... more

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