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Euler Formula

"One formula that is used frequently to rewrite a complex number is the Euler Formula. The Euler Formula can be used to convert a complex number from exponential form to rectangular form and back. The ...

Equation of a Circle

"A circle can't be represented by a function, as proved by the vertical line test. However, we can obtain an equation that describes the full circle by using the distance formula between the given cen ...

Secant and Cosecant

"To graph secant and cosecant, find values of the reciprocal functions and plot them on the coordinate plane. Unlike the graphs of sine and cosine, secant and cosecant have vertical asymptotes wheneve ...

Double Angle Formulas

"The double angles sin(2theta) and cos(2theta) can be rewritten as sin(theta+theta) and cos(theta+theta). Applying the cosine and sine addition formulas, we find that sin(2theta)=2sin(theta)cos(theta ...

Distance Formula

"Using what we know about the Pythagorean theorem, we are able to derive the distance formula which is used to find the straight distance between two points in a coordinate plane. The distance formu ...

Reciprocal Trigonometric Functions

"There are three reciprocal trigonometric functions, making a total of six including cosine, sine, and tangent. The reciprocal cosine function is secant: sec(theta)=1/cos(theta). The reciprocal sine ...

DeMoivre's Theorem

"We know how to multiply complex numbers, but raising complex numbers to a high integer power would involve a lot of computation. Fortunately we have DeMoivre's Theorem, which gives us a more simple s ...

Radian Angle Measure

"An angle is the figure formed by two rays with a common endpoint. We typically use degree measures when measuring angles, however we can use radian angle measure as an alternate way of measuring angl ...

Pythagorean Theorem Proofs

"The Pythagorean theorem states that in a right triangle the sum of its squared legs equals the square of its hypotenuse. The Pythagorean theorem is one of the most well-known theorems in mathematics ...

Pythagorean Theorem Converse

"If we know that the sum of two square sides in a triangle equals the square of the third side, we can conclude that the triangle is a right triangle. Pythagorean triples are commonly seen side length ...

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