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The trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its ... more

The trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its ... 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/

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the ... more

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

The altitude of a triangle is the distance from a vertex perpendicular to the opposite side. There is a relation between the altitude and the sides of the ... more

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). Median of a triangle is a line ... more

Triangle is a polygon with three edges and three vertices. The area of a triangle with base length b and height length h is given by multiplying base ... more

In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, ... 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.