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Mean anomaly

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. ... more

Sliding gravity conveyer

calculates the speed of sliding of materials on a gravity conveyer

... more

Exponential Decay (with half-life)

Half-life is the amount of time required for the amount of something to fall to half its initial value. The term is very commonly used in nuclear physics ... more

Logarithmic Mean Temperature Difference

The logarithmic mean temperature difference (also known as log mean temperature difference or simply by its initialism LMTD) is ... more

Energy of damped harmonic motion

Damped harmonic motion is a real oscillation, in which an object is hanging on a spring. Because of the existence of internal friction and air resistance, ... more

Mean anomaly - function of gravitational parameter

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. ... more

Subtraction - 10 objects/subtrahend version

Subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then ... more

Maximum thermal efficiency of a Diesel cycle

The Diesel cycle is a combustion process of a reciprocating internal combustion engine. In it, fuel is ignited by heat generated by compressing air in the ... 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/

West number

The West number is an empirical parameter used to characterize the performance of Stirling engines and other Stirling systems. A Stirling engine is a heat ... more

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