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The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect ... more
The dynamic (shear) viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different ... more
The magnetic diffusivity is a parameter in plasma physics which appears in the magnetic Reynolds number.
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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 fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal “forces” or so-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/
The Peng–Robinson equation of state (PR EOS) was developed in 1976 at The University of Alberta by Ding-Yu Peng and Donald ... more
When a driver is driving on a sag curve at night, the sight distance is limited by the higher grade in front of the vehicle. This distance must be long ... more
When a driver is driving on a sag curve at night, the sight distance is limited by the higher grade in front of the vehicle. This distance must be long ... more
The stiffness of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (for ... 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.