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n mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more

n mathematics, the Klein bottle is an example of a non-orientable surface, informally, it is a surface (a two-dimensional manifold) in which notions of ... more

In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell ... more

In engineering, deflection is the degree to which a structural element is displaced under a load.

This maximum deflection occurs at a distance x_1
... more

In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more

The Herschel–Bulkley fluid is a generalized model of a non-Newtonian fluid, in which the strain experienced by the fluid is related to the stress in a ... more

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:

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

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:

For **y** axis:

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/

“Clearing the neighbourhood around its orbit” is a criterion for a celestial body to be considered a planet in the Solar System. This was one ... more

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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 by20 degrees, then the objects in the map will correspondingly rotate20 degreesclockwise. Find the new coordinates of the character.