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he decibel is a logarithmic unit used to express the ratio between two values of a physical quantity. The bel represents a ratio between two power ... more

Subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then ... more

Every single thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to its ... more

The Sagnac effect (also called Sagnac interference), named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is ... more

The surface gravity, g, of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought ... more

An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or ... more

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:

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

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:

For **y** axis:

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/

Wien’s displacement law states that the black body radiation curve for different temperature peaks at a wavelength that is inversely proportional to ... more

Flow rate is defined to be the volume of fluid passing by some location through an area during a period of time.

The change in volume is the amount
... more

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

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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 by20 degrees, then the objects in the map will correspondingly rotate20 degreesclockwise. Find the new coordinates of the character.