'

Search results

Found 659 matches
Bend Deduction - right angles

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

Low-density lipoprotein - Estimation of LDL particles via cholesterol content - in mmol/l

Low-density lipoprotein (LDL) is one of the five major groups of lipoproteins. These groups, from least dense to most dense, are: ... more

Low-density lipoprotein - Estimation of LDL particles via cholesterol content - in mg/dl

Low-density lipoprotein (LDL) is one of the five major groups of lipoproteins. These groups, from least dense to most dense, are: ... more

Properties of concrete - modulus of elasticity

Concrete has relatively high compressive strength, but significantly lower tensile strength. As a result, without compensating, concrete would almost ... more

Tsiolkovsky rocket equation - acceleration based

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that ... more

Height of a trapezoid in relation with the sides

Trapezoid is a convex quadrilateral with only one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides ... more

Declination of the Sun

The position of the Sun in the sky is a function of both time and the geographic coordinates of the observer on the surface of the Earth. As the Earth ... more

Declination of the Sun (simplified)

The position of the Sun in the sky is a function of both time and the geographic coordinates of the observer on the surface of the Earth. As the Earth ... 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/

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

Create a new formula