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A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical ... more
A square wave is a non-sinusoidal periodic waveform (which can be represented as an infinite summation of sinusoidal waves), in which the amplitude ... more
In radiometry, radiant exitance is the radiant flux emitted by a surface per unit area, and spectral exitance is the radiant exitance of a surface per unit ... 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 fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or ... more
Counter-electromotive force (abbreviated counter EMF or simply CEMF), also known as back electromotive ... more
The position of the Sun in the sky is a function of both time and the geographic coordinates of the observer on the surface of the Earth. As the Earth ... more
The position of the Sun in the sky is a function of both time and the geographic coordinates of the observer on the surface of the Earth. As the Earth ... more
In structural engineering, a structure is a body or combination of pieces of rigid bodies in space to form a fitness system for supporting loads. ... more
The Huygens–Fresnel principle is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction. ... 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.