[PDF] Top 20 On Transforming Spirographic Output with Trigonometric and Other Functions

... International Journal of Computer Applications 0975 – 8887 Volume 60– No.13, December 2012 and by controlling the realization of pixels on the basis of a condition on the variable t, one[r] ... See full document

... In 1885, circulant matrix was first proposed by Muir, and he did some basic research. Until 1950–1955, Good et al. began to study the inverse, determinants and characteristic values of circulant matrices; these efforts ... See full document

... 1 The trigonometric functions are continuous on their respective domains.[r] ... See full document

... fractional trigonometric function analysis and fractional derivative of fractional Weierstrass func- tion by Jumarie fractional derivative, establishes that roughness indices are invariant to this ge- ... See full document

... method, trigonometric substitution method, ...of trigonometric functions, which are not easy to obtain their answers using the methods mentioned ... See full document

... exponential functions exp ( ) x and exp ( ) − x called hyperbolic ...These functions which arise in various engineering applications, have many properties in common with the trigonometric func- ... See full document

... algebraic functions. They did not study limits involving trigonometric functions, as they were not included in their ...of other functions such as exponential, logarithmic and ... See full document

... of functions was introduced as a new approach to extensions of the summation of real and complex functions, and also evaluating ...summand functions generalize the (logarithm of) Gamma-type ... See full document

... quadratic trigonometric polynomial blending functions where we include a tension parameter, the latter is mainly important for object ...blending functions are useful for constructing ... See full document

... inverse trigonometric functions, we show that the new inequalities presented in this paper are more refined than that obtained in earlier ...metric functions and hyperbolic functions in our ... See full document

... many functions which are not one-one, onto or both and hence we can not talk of their ...that trigonometric functions are not one-one and onto over their natural domains and ranges and hence their ... See full document

... Heywood, “On the integrability of functions defined by trigonometric series,” The Quarterly Journal of Mathematics, vol.. Chen, “On the integrability of functions defined by trigonometri[r] ... See full document

... The article considers six types of integrals related with the powers of trigonometric functions. We can obtain the infinite series expressions of these integrals by using Taylor series expansions and ... See full document

... involving trigonometric and inverse trigonometric functions play an impor- tant role and have many applications in science and engineering [2, 8, 12, 17–19, ... See full document

... The study of Jordan’s and Kober’s inequality and inequalities of trigonometric functions has a rich literature, for example, [1, 2, 4, 6, 7, 8, 9, 10, 11] and references therein. There are many refinements, ... See full document

... u, v, respectively. Now we can apply Lemma 3.6. First assume that 3.29 holds and consider the cases i, ii, iii, and iv of Lemma 3.6. For the case i, it follows from 30, Page 61, Theorem 1 that the initial values u, v of ... See full document

... involving trigonometric and hyperbolic inequalities have attracted attention of several ...for trigonometric and hyperbolic func- tions have been studied extensively in numerous ... See full document

... Functions (.) and (.) can be found (see [], Chapter , [], p. and [–]). Another pair of lemniscate functions, the arc lemniscate tangent arctl and the hyperbolic arc lemniscate tangent arctlh, ... See full document

... a trigonometric ratio for angles expressed in degrees that are multiples of 0º, 30º, 45º, 60º or 90º, or for angles expressed in radians that are multiples of 0, , and explain the ... See full document

... of functions involving sine function, cosine function and tangent function, six inequalities involving tangent func- tion, cotangent function, sine function, secant function and cosecant function are ... See full document