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The normal segment for a given line is defined to be the line segment drawn from the origin perpendicular to the line. This segment joins the origin with ... more

In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. It consists of the set of points equidistant from a fixed central point in ... more

Distance is a numerical description of how far apart objects are. In analytic geometry, the distance between two points of the xy-plane can be found using ... more

In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

... moreTo 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 Â© 2014 David Lippman and Melonie Rasmussen

http://www.opentextbookstore.com/precalc/

Creative Commons License : http://creativecommons.org/licenses/by-sa/3.0/us/

A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the ... more

A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the ... more

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... more

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... 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.