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How To Find the Polar Form of a Complex Number

Graph showing a complex number graphed in rectangular coordinates

Polar form is a way of representing complex numbers by graphing them. But before determining how to find the polar form, we must first establish what a complex number is. A complex number is a trigonometry concept that means a “combination of real numbers and imaginary numbers.” Real numbers can be positive or negative. They are essentially any quantifiable number that, when squared, results in a positive value.

Imaginary numbers are numbers that don't compute on a calculator. When squared, they result in a negative value. Because these numbers are imaginary, they cannot be expressed with numerical values. Instead, the unit used for imaginary numbers is i, the square root of -1. Here are some examples of imaginary numbers: 5i, 3.6i, −14.3i, (√7)i, 2,891i. All of these numbers have been multiplied by the value of i or √−1.

Complex numbers have a real part and an imaginary part. Complex number z is used to represent the combined result of the real and imaginary parts. Here are some examples of complex numbers:

polar form: Example of a complex number

Example of a complex number

Example of a complex number

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How To Find the Third Side of a Triangle in 3 Ways

how to find the third side of a triangle: graph of the law of sines

There are several different ways you can compute the length of the third side of a triangle. Depending on whether you need to know how to find the third side of a triangle on an isosceles triangle or a right triangle, or if you have two sides or two known angles, this article will review the formulas that you need to know.

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What Is the Domain of Tangent, Sine, and Cosine?

domain of tangent: graph of three reciprocal functions

The main three trigonometric functions are the sine function, cosine function, and tangent function, sometimes represented as sin x, cos x, and tan x. These functions measure the ratio between different sides of a triangle. The easiest way to memorize these trigonometric functions is the mnemonic device SOHCAHTOA:

Sine = Opposite over Hypotenuse

Cosine = Adjacent over Hypotenuse

Tan = Opposite over Adjacent

Understanding tangent, sine, and cosine as functions enables us to figure out the range and domain of tangent, sine, and cosine.

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Learn How To Find the Area of a Non-Right Triangle

area of a non right triangle: Diagram of a right triangle

To find the area of a non-right triangle, let’s first review the standard area formula of a right triangle. A right triangle is made up of three sides: the base, the height, and the hypotenuse. To get the area of a triangle you must multiply the two adjacent side lengths of the 90° angle, which are the base and the height of the triangle, and divide this quantity by half. This is the formula for the area of a right triangle:

Formula for the area of a right triangle

However, this formula doesn't work as effectively for acute and obtuse angles. So here's how to find the area of a non-right triangle.

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How To Find the Base of a Triangle in 4 Different Ways

how to find the base of a triangle: Mathematical diagram of a right-angled triangle

Depending on whether you're studying the area of a triangle, the Pythagorean Theorem, or advanced trigonometry in your high school math class, there are many ways to find the base of a triangle. Here are a couple of the most common scenarios and methods:

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