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The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish ... more

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may ... more

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

A graveyard orbit, also called a junk orbit or disposal orbit, is a supersynchronous orbit that lies significantly above synchronous orbit, where ... more

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. It can be ... more

In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. It can be ... 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/

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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.