Radian and Measure for angles

An angle can be represented in terms of degrees or radians. A complete revolution around a circle is equal to 360 degrees or 2π radians.
The radian is a measure of angle that is defined in terms of the radius and the arc length. When the length of the arc is equal to the radius of the circle, the angle subtended is 1 radian.
To convert between degrees and radians, remember that 180 degrees = π radians. Therefore, to convert degrees to radians, multiply by π/180, and to convert radians to degrees, multiply by 180/π.

Trigonometric functions such as sine, cosine and tangent, when applied to angles measured in radians, have properties and behaviours that are frequently exploited in mathematics, particularly in calculus and the study of periodic phenomena.
When calculating arc length, use the formula s = rθ, where s is arc length, r is radius, and θ is the angle in radians.
The area of a sector can be calculated using the formula A = 0.5*r²θ, again with θ measured in radians.

Euler’s Formula states that for any real number x, e^(ix) = cos x + i sin x. This formula connects complex numbers, exponentials and trigonometry, and is fundamental to much of mathematics and physics.
Using Euler’s Formula, complex numbers can be represented in the exponential form re^(iθ) instead of the polar form, r(cos θ + i sin θ), where r is the modulus and θ is the argument. The two forms are equivalent, but the exponential form is often more convenient to work with.
Complex numbers in exponential form can be easily multiplied and divided by simple addition and subtraction of their arguments (measured in radians).

The argument of a complex number refers to the angle it makes with the real axis in the anticlockwise direction, when represented as a point in the complex plane. Note that angles in mathematics are often measured in radians.
When a complex number is multiplied by e^(iθ), shift the argument of the complex number by an angle of θ. Consequently, multiplication by e^(iθ) has a simple geometric interpretation: it rotates the complex number in the complex plane.