'

Search results

Found 479 matches
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/

Solute sieving coefficient

The selection of synthetic membranes for a targeted separation process is usually based on few requirements. Membranes have to provide enough mass transfer ... more

Seismic moment

Seismic moment is a quantity to measure the size of an earthquake and is proportional to the area of the rupture times the average slip that took place ... more

Corner sight distance

Corner sight distance (CSD) is the road alignment specification which provides a substantially clear line of sight so that the ... more

Magnitude of proper motion

Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the ... more

Mean anomaly at epoch

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

Radial Thermal Resistance in composite walls (conduction)

Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance ... more

Percentage Change

The terms “relative change” and “relative difference” are used to compare two quantities while taking into account the ... more

Surface wave magnitude scale

The surface wave magnitude (M_s) scale is one of the magnitude scales used in seismology to describe the size of an earthquake. It is based on measurements ... more

Reed's Law

Reed’s law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size ... more

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

Create a new formula