Search results
In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, ... more
An acousto-optic deflector spatially controls the optical beam. In the operation of an Acoustic-optic deflector the power driving the acoustic transducer ... more
Birch’s law establishes a linear relation of the compressional wave velocity of rocks and minerals of a constant average atomic weight with density ... more
Plane waves in vacuum are the simplest case of wave propagation: no geometric constraint, no interaction with a transmitting medium. For electromagnetic ... more
In electromagnetics, an antenna’s power gain or simply gain is a key performance figure which combines the antenna’s directivity and electrical ... more
The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... more
The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... 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/
Acoustic impedance is the measure of the opposition that a system presents to an acoustic flow when an acoustic pressure is applied to it. Acoustic ... more
A spherical polygon on the surface of the sphere is defined by a number of great circle arcs which are the intersection of the surface with planes through ... more
...can't find what you're looking for?
Create a new formula
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.