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Absolute magnitude is the measure of a celestial object’s intrinsic brightness. It is the hypothetical apparent magnitude of an object at a standard ... more

In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed ... more

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may ... 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/

Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex ... more

Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex ... more

Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more

An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant ... more

Rhombus is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length. Every rhombus is a parallelogram, and a rhombus with ... more

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term complex impedance may be ... more

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term complex impedance may be ... more

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term complex impedance may be ... 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

The law of cosines relates the cosine of an angle to the opposite side of an arbitrary triangle and the length of the triangle’s sides.

The law
... more

In mathematics, the Pythagorean theorem, also known as Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among the three sides of ... 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

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. If the internal ... more

The law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.The law of ... more

Roll-off is the steepness of a transmission function with frequency, particularly in electrical network analysis, and most especially in connection with ... more

In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. It is a four-sided figure in which ... more

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Parallelogram is a simple (non self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of ... more

Square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles). It can also be ... more

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral ... more

Law of sines is an equation relating the lengths of the sides of any shaped triangle to the sines of its angles. The law of sines can be used to compute ... more

In geometry, Napoleon’s theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, ... more

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more

In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose ... 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.