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Current (AC-rms)

The RMS current for sinusoidal systems can be described mathematically as a function of peak current.

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Drake equation

is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy

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Micro chevron (MC) test (critical energy release rate)

The wafer bond characterization is based on different methods and tests. Wafer bonds are commonly characterized by three important encapsulation ... 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

Brushed DC electric motor - Torque

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

Current gain - simplified formula (for equal impedances)

The current gain can be calculated using current instead of power using Joule’s first law to calculate. In many cases, the input and output ... more

Churchill–Bernstein Equation

The equation yields the surface averaged Nusselt number, which is used to determine the average convective heat transfer coefficient. Newton’s law of ... more

Coil magnetic energy

The magnetic energy stored by a coil carrying a current is given by one half of the inductance of the coil times the square of the current

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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

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
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Bretschneider's formula - Area of a general quadrilateral

In geometry, Bretschneider’s formula is the shown expression for the area of a general quadrilateral.

A quadrilateral is a polygon with four ... more

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