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Parameterize a Circle

"One application of parametric equations that is useful to learn is how to parameterize a circle. In order to parameterize a circle centered at the origin, oriented counter-clockwise, all we need to k ...

Parameterize

Hipervinculo Matemáticas

Parameterize

"There are some situations that are useful to learn to parameterize. We commonly parameterize line segments, and require knowledge of the starting and ending positions. In order to understand how to p ...

Parallel Lines in Space

"With the introduction of the 3D coordinate system we find the concepts of skew, perpendicular and parallel lines in space. Skew lines are new, and are lines that are not parallel, yet never intersect ...

Other Forms of the Cosine Double-Angle Formula

"The cosine double angle formula is cos(2theta)=cos2(theta) - sin2(theta). Combining this formula with the Pythagorean Identity, cos2(theta) + sin2(theta)=1, two other forms appear: cos(2theta)=2cos2 ...

Navigation Problems

"The word problems encountered most often with vectors are navigation problems. These navigation problems use variables like speed and direction to form vectors for computation. Some navigation proble ...

Natural Logarithm

"The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. Natural logarithms are special types of logarithms and are used in solving time an ...

Multiplication of Vectors

"The addition and scalar multiplication of vectors are basic operations that can be done using their geometric or the algebraic representations. When looking at the geometric representation we can und ...

Motion Along a Line

"We can use the vector equation of a line to describe the motion along a line. We can also rewrite these equations to represent the motion along a line as a parametric equation. In order to create a v ...

Asymptotes of Secant, Cosecant, and Cotangent

"To find the x-intercepts and asymptotes of secant, cosecant, and cotangent, rewrite them in terms of sine and cosine. Notice that since secant and cosecant have 1 in the numerator and a trig functio ...

Arithmetic Series

"We can use what we know of arithmetic sequences to understand arithmetic series. An arithmetic series is a series or summation that sums the terms of an arithmetic sequence. There are methods and for ...

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