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Triangle wave (in trigonometric terms)

A triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square ... more

Logarithm of the odds ratio

The logit function is the inverse of the sigmoidal “logistic” function or logistic transform used in mathematics, especially in statistics. ... more

Pythagorean theorem (arbitrary triangle - acute angle)

Generalization of the Pythagorean theorem for the side opposite of the acute angle of an arbitrary triangle

... more

Pythagorean theorem (arbitrary triangle - obtuse angle)

Generalization of the Pythagorean theorem for the side opposite of the obtuse angle of an arbitrary triangle

... 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/

Logit function

The logit function is the inverse of the sigmoidal “logistic” function or logistic transform used in mathematics, especially in statistics. ... more

Gas in a box (momentum)

The particle in a box model describes a particle free to move in a small space surrounded by impenetrable barriers. the results of the quantum particle in ... more

Morley's trisector theorem (area)

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, ... more

Morley's trisector theorem

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral ... more

Möbius strip (y- coordinate )

The Möbius strip or Möbius band, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being ... more

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