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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 trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. ... more
Circular segment is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord. More formally, a Circular ... more
Circular segment is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord. More formally, a circular ... 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
Circular arc is a segment of a circle. A circular sector or circle sector is the portion of a disk enclosed by two radii and an arc, where the smaller area ... more
Circular segment is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord. More formally, a Circular segment is a ... 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 mathematics, the Pythagorean theorem, also known as Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among the three sides of ... more
In mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more
In mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more
n mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more
A spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge’s base). The angle between ... more
A spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge’s base). The angle between the ... more
In mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions 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/
A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more
A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more
Compton scattering is an inelastic scattering of a photon by a free charged particle, usually an electron. It results in a decrease in energy (increase in ... more
In mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more
In mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more
n mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more
n mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more
In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.
It was first ... 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
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
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
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
Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, ... 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.