'

Search results

Found 1471 matches
Resonant frequency of string

Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own ... more

Quartic equation

Solves a univariate polynomial equation of the fourth degree. (For possitive values of x)

... more

Cubic equation

Solves a univariate polynomial equation of the third degree.

... more

FPM to CFM Calculator

Online FPM to CFM unit converter calculator helps to convert cubic feet per minute from feet per minute.

... more

Fermi–Dirac distribution

Fermi–Dirac statistics describes a distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli ... more

Bose–Einstein statistics ( εi > μ)

In quantum statistics, Bose–Einstein statistics (or more colloquially B–E statistics) is one of two possible ways in which a collection of non-interacting ... more

Worksheet 334

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.

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:

Pythagorean theorem (right triangle)

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

Cosine function
Subtraction

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:

Cosine function

For y axis:

Sine function

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/

Area of a Hemisphere

A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a completely round ball. A sphere is ... more

Lead angle

Lead is the axial advance of a helix or screw during one complete turn (360°). The lead for a screw thread is the axial travel for a single revolution. ... more

Area Moment of Inertia - Filled Right Triangle

The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a ... more

...can't find what you're looking for?

Create a new formula