Search results
In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a ... more
Envy ratio in finance is the ratio of the price paid by investors to that paid by the management team for their respective shares of the equity. This ... more
The Fourier number (Fo) or Fourier modulus, is a dimensionless number that characterizes heat conduction. It is the ratio of diffusive/conductive ... more
For periodic compounding, the exact doubling time for an interest rate of r per period is a logarithmic formula, that can be used if we want to know the ... more
Thermal expansion is the tendency of matter to change in length, area or volume in response to a change in temperature, through heat transfer.
The
... more
In petrophysics, Archie’s law relates the in-situ electrical conductivity of a sedimentary rock to its porosity and brine saturation as shown ... 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 finance, return is a profit on an investment. return is also used to refer to a profit on an investment, expressed as a proportion of the amount ... more
In finance, leverage is a general term for any technique to multiply gains and losses. Most often it involves buying more of an asset by using borrowed ... more
In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell ... 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.