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In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more

In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ... more

Eccentricity e of the cylindric section and semi-major axis of the cylindric section depend on the radius of the cylinder and the angle between the secant ... more

In physics, the Coriolis effect is a deflection of moving objects when they are viewed in a rotating reference frame.

An air or water mass moving with
... more

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.

It was first ... 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/

The beta angle is a measurement that is used most notably in spaceflight. The beta angle determines the percentage of time an object such as a spacecraft ... more

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... 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.