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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
Rhombus is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length. The can be calculated by the semi perimeter and the ... more
A rhombus is a simple (non-self-intersecting) quadrilateral all of whose four sides have the same length. A perimeter of a rhombus is a path that surrounds ... more
The inradius (the radius of the incircle of the rhombus) can be expressed in terms of the diagonals.
... more
The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly ... more
A triangle is a polygon with three edges and three vertices. In a scalene triangle, all sides are unequal and equivalently all angles are unequal. The area ... more
Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, ... more
In geometry, Bretschneider’s formula is the shown expression for the area of a general quadrilateral.
A quadrilateral is a polygon with four ... more
A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree ... 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
The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The circumcenter of a triangle ... more
A quadrilateral is a polygon with four sides (or edges) and four vertices or corners.The area of a convex quadrilateral can be expressed in terms of the ... more
Quadrilateral is a polygon with four sides (or edges) and four vertices or corners. The area of a quadrilateral can be calculated by the sides and the ... more
A triangle is a polygon with three edges and three vertices. In a scalene triangle, all sides are unequal and equivalently all angles are unequal. When the ... more
The area of an arbitrary triangle can be calculated from the two sides of the triangle and the included angle.... more
The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The circumcenter of a triangle ... more
Altitude of a triangle is a straight line through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). The area of ... more
A circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. Its radius is called the ... 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
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/
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
A heptagon (or septagon) is a polygon with seven sides and seven angles. In a regular heptagon, in which all sides and all angles are equal, the sides meet ... more
The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a ... 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
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
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
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
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
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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 by 20 degrees, then the objects in the map will correspondingly rotate 20 degrees clockwise. Find the new coordinates of the character.