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In mathematics, the Pythagorean theorem, also known as Pythagoras’ theorem, is a fundamental relation in Euclidean geometry among the three sides of ... 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
The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is ... more
A triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.
Like a
... more
In geometry, Heron’s formula (sometimes called Hero’s formula), named after Hero of Alexandria, gives the area of a triangle by requiring no ... more
In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.
1.The orbit of a ... more
A circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is called ... 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/
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
A Reuleaux triangle is a curve of constant width,( the separation of two parallel lines tangent to the curve is independent of their orientation), based ... 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.