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Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more
In mathematics, Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.
P(x)=ax^2 + bx + c,
In mathematics, Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.
P(x)=ax^2 + bx + c,
In mathematics, a hyperboloid is a quadric – a type of surface in three dimensions – . A hyperboloid of revolution of one sheet can be obtained by ... more
In mathematics, a hyperboloid is a quadric – a type of surface in three dimensions – . A hyperboloid of revolution of two sheets can be obtained by ... 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 dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more
The coefficient B(T,P) used in the UNESCO equation, speed of sound in sea water), depends on the temperature and the pressure
... more
A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... more
In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The common exponential ... 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.