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Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... 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/

Lead is the axial advance of a helix or screw during one complete turn (360°). The lead for a screw thread is the axial travel for a single revolution. ... more

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large ... more

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

In mathematics, the beta function, also called the Euler integral of the first kind, is a special function.The beta function was studied by Euler and ... more

The depth of focus (or depth of field) is a lens optics concept that measures the tolerance of placement of the image plane (the film plane in a camera) in ... more

Calculates the volume of a hollow sphere. A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape ... more

The Archimedean spiral is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed ... more

Log-polar coordinates in the plane consist of a pair of real numbers (ρ,θ), where ρ is the logarithm of the distance between a given point and the origin ... 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.