Three major techniques are employed to calculate [pi]. Namely, (i) the perimeter of polygons inscribed or circumscribed in a circle, (ii) calculus based methods using integral representations of inverse trigonometric functions, and (iii) modular identities derived from the transformation theory of elliptic integrals. This note presents a…

In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the derivative of the exponential functions and the derivative of their inverses, the logarithmic functions. I extend this approach to generate formulae for the…

The graph of this function is analyzed by using calculus methods and the computer. The graph in most texts is shown to be misleading. (MP)

Methods are presented for teaching the meaning of exponential functions, Euler's formula, De Moivre's theorem and Maclaurin's series for exponentials, cosine, and sine to juniors or seniors in high school. (JG)

Presents a situation in which differential calculus is used with inverse trigonometric tangent functions to maximize an angle measure. A negative distance measure ultimately results, requiring a reconsideration of assumptions inherent in the initial figure. (Author/MKR)

An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…

Theorems about the hyperbola which are ordinarily introduced in calculus courses can be proved without using the calculus. (SD)

This is part one of a three-part SMSG calculus text for high school students. The aim of the text is to develop some of the concepts and techniques which will enable the student to obtain important information about graphs of elementary functions. Chapter topics include: (1) polynomial functions; (2) the derivative of a polynomial function; and…

An old way to determine asymptotes for curves described in polar coordinates is presented. Practice in solving trigonometric equations, in differentiation, and in calculating limits is involved. (MNS)

Describes a project in which trigonometry and precalculus students cooperate to measure the height of an inaccessible water tower. (MKR)

Presents a solution to the problem of finding the probability that a needle would cross a crack in a tile floor when dropped. (MKR)

Presents problems to find the integrals of logarithmic and inverse trigonometric functions early in the calculus sequence by using the Fundamental Theorem of Calculus and the concept of area, and without the use of integration by parts. (Author/ASK)