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Instantaneous current for L2 (Three-phase electric application)

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time ... more

Brushed DC electric motor - Voltage balance

A brushed DC motor is an internally commutated electric motor designed to be run from a direct current power source. Brushed motors were the first ... more

Time-varying instantaneous voltages for L1 (Three-phase electric application)

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time ... more

Time-varying instantaneous voltages for L3 (Three-phase electric application)

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time ... more

Time-varying instantaneous voltages for L2 (Three-phase electric application)

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time ... 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 Â© 2014 David Lippman and Melonie Rasmussen
http://www.opentextbookstore.com/precalc/

Self-inductance factor

Self inductance factor of a solenoid depends on the number of turns, the cross section area, the length of the solenoid and the material within the solenoid

... more

Emf Induced in a Generator Coil

Electric generators induce an emf by rotating a coil in a magnetic field. Electromotive force, also called Emf, is the voltage developed by any source of ... more

Solar cell - current delivered by the illuminated diode

Operation of a solar cell can be understood from the equivalent circuit at right. Light, of sufficient energy (greater than the bandgap of the material), ... more

RC circuit (Voltage of the capacitor at Series circuit

A resistorâ€“capacitor circuit (RC circuit), or RC filter, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. ... more

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