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Vertex of a Parabola

"In order to graph a parabola, we need to find several pieces of information, including the vertex. One way to find the vertex of a parabola is to turn the standard form of the quadratic equation into ...

Velocity and Acceleration

"If position is given by a function p(x), then the velocity is the first derivative of that function, and the acceleration is the second derivative. By using differential equations with either velocit ...

Using Trigonometric Identities

"When simplifying problems that have reciprocal trig functions, start by substituting in the identities for each. If possible, write tangent in terms of sine and cosine. Use algebra to eliminate any ...

Using the Sine and Cosine Addition Formulas to Prove Identities

":Applying the cosine addition and sine addition formulas proves the cofunction, add pi, and supplementary angle identities. Using the formulas, we see that sin(pi/2-x) = cos(x), cos(pi/2-x) = sin(x) ...

Unit Vectors

"One special type of vectors are unit vectors. Unit vectors have a magnitude of one, and the specific unit vectors i and j represent the positive horizontal and vertical unit vectors in a two dimensio ...

Trigonometric Identities

"Identities are equations true for any value of the variable. Since a right triangle drawn in the unit circle has a hypotenuse of length 1, we define the trigonometric identies x=cos(theta) and y=sin( ...

Trigonometric Form of Complex Numbers

"A convenient form for numbers in the complex plane, other than rectangular form, is the trigonometric form of complex numbers. The trigonometric form of complex numbers uses the modulus and an angle ...

Tricky Substitutions Involving Radicals

"When an indefinite integral involves a function of x times the radical of another function of x, the substitution method must be used in multiple ways. In these tricky substitutions involving radical ...

Introduction to Sequences

"Lists of numbers, both finite and infinite, that follow certain rules are called sequences. This introduction to sequences covers the definition of a sequence and how to identify a rule. There are sp ...

Introduction to Polynomials

"Before adding and subtracting polynomials or multiplying polynomials, it is important to have an introduction to polynomials with a definition of a polynomial and polynomial vocabulary. Importan ...

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