Ask Dr. Math College Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

 TOPICS This page:   trigonometry    Search   Dr. Math See also the Dr. Math FAQ:   trigonometry formulas Internet Library:   trigonometry COLLEGE Algorithms Analysis Algebra    linear algebra    modern algebra Calculus Definitions Discrete Math Exponents Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean Imaginary/Complex   Numbers Logic/Set Theory Number Theory Physics Probability Statistics Trigonometry Browse College Trigonometry Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     DeMoivre's theorem. Counting Extrema [10/23/1996] Find the number of minima and maxima of the function [Sin Na/Sin a]^2 on the interval [0, pi]. Curious Property of a Regular Heptagon [04/06/2001] How can I prove that in a regular heptagon ABCDEFG, (1/AB)=(1/AC)+(1/ AD)? Proving Identities Rigorously [01/23/2002] I've been taught that the proper way to work on identities is to work with one side at a time only. Trigonometric Identities [11/13/1997] Do you have any suggestions for finding an easy way to remember them that I could apply to all identities? Algebraic Expression for cos(arctan(x)/3) [8/15/1996] How do I find an algebraic expression for cos(arctan(x)/3) so that I can get rid of the trigonometric operands? Amplitude of Function with Sine and Cosine [01/11/2004] How do you predict the amplitude of a function involving both sine and cosine? For instance, how is it possible to find the amplitude of f(x) = a*sin(x) + b*cos(x) without using an automatic grapher? Arccos [08/23/1997] Please solve: Arc cos (cos y) + Arc sin (sin x) = y + x. Asin/acos/atan for Complex Numbers [3/27/1996] How do you find asin(x+iy), acos(x+iy), and atan(x+iy)? Bretschneider's Theorem and Cyclic Quadrilaterals [11/30/2000] Can you prove Bretschneider's Theorem for the area of a quadrilateral? Also, can you show that any quadrilateral with supplementary opposing angles can be inscribed in a circle? Building a Circular Horse Pen [06/16/2002] My Dad and I are building a round pen for our horse. We have 16 16ft. panels and a 10 ft. gate and a 4ft. gate. (270 ft. total) We want to use a radius and mark the places to dig holes for each post that will support the panels, but we don't know how long the radius should be. Can you help? Catenary and Parabola Comparison [04/06/2004] What is the difference between a catenary and a parabola? I don't know the difference in shape. Why is the St. Louis arch a catenary and not a parabola? Catenary Curve [03/30/1999] Find the vertex of a catenary curve. A Change of Variables [05/05/2003] How do I solve int(sin^5(2x)cos(2x)dx) ? Circle on a Sphere Equation [05/05/2000] How can I find an equation for all points that fall within a given radius from a single latitude and longitude on the surface of a sphere? Circles on the Surface of a Sphere [08/11/1999] How can I convert the equation of a circle on a unit sphere in the (X,Y,Z) coordinate system into a function that is defined in terms of spherical coordinates theta and phi? Closed Form of Complex Function [03/24/2003] I would like a closed form (not a power series) for f(z) such that f is analytic and f(z) = 0 when z = (k*pi)^3, z = ((k*pi)^3)e^i2*pi/3, and z = ((k*pi)^3)e^i4*pi/3 where k is a positive integer. Complex Variables [03/25/2003] Is there any complex root for an equation like sin(x)=3/2? What does a^i= ? where a is a real constant. Computing Angles of a Right Triangle [09/04/1997] Is there a way to compute the other two angles of a right triangle without a calculator? If a table is required, where can I find it? Convergence of Product of Sines [10/17/2003] Prove that (sin(pi/n))*(sin(2pi/n))*...*(sin((n-1)pi/n)) = n/(2^(n-1)) for n >= 2. de Moivre's Formula [08/11/2002] How do I use de Moivre's formula to express cos(3p) and sin(3p) in terms of cos p and sin p? And why would this be useful? Derivation of Law of Sines and Cosines [11/02/1997] How do you derive the law of sines and the law of cosines? Deriving Lagrange's Trig Identity [01/09/2004] Using the identity 1 + z + z^2 + ... + z^n = (1 - z^(n+1))/(1 - z), z not = 1, derive Lagrange's trig identity: 1 + cosx + cos(2x) + ... + cos(nx) = 1/2 + (sin[(2n+1)x/2])/(2sin(x/2)) where 0 < x < 2*pi. Deriving the Haversine Formula [04/21/1999] I need to write a program module to calculate distances given longitude and latitude data, trying to find an object within a mile's radius of its location. Deriving Trigonometric Identities [07/20/2008] How do you derive the sum-to-product and product-to-sum identities in trigonometry? Difference Between arsinh and arcsinh Functions [05/13/2004] Why isn't there a "c" in arsinh, arcosh, and artanh? These are the equivalents of arcsin, arccos and arctan but they are hyperbolic. Differing Definitions of arcsec(x) Lead to Confusion over Signs [12/03/2005] I was trying to prove the derivative of arcsec(x), and according to my book sec(arcsec x) equals |x|, but I think it should just be x. Can you explain what I'm missing? Domain of Arccot [05/23/2002] Why is the arccot function defined over 0 to pi, rather than from -pi/2 to pi/2? Euler in the Product of a Regular Polygon's Diagonal Lengths [04/06/2010] A professor emeritus considers an n-sided regular polygon A1, A2, ... An inscribed in the unit circle; and conjectures that the product of the lengths of its diagonals equals n. By defining the polynomial f(x) as the product of x - r over its (n - 1) roots, and applying complex numbers and Euler's equation, Doctor Vogler proves that sin(pi/n) * sin(2pi/n) * ... * sin[(n - 1)pi/n] = n/2^(n - 1). Exact Sin [11/19/2014] An adult familiar with double- and half-angle trigonometry identities seeks a closed form expression for sin(100). Doctor Carter outlines an approach that starts with a derivation of the triple angle formula. Explaining the Dot Product [04/05/1998] Exactly what does the dot product represent? Find a Function, Integrals [12/17/1997] Suppose the graph of f has the formula f(x)=-x+1 for 0<=x<=1; x-1 for 1]

Search the Dr. Math Library:

 Search: entire archive just College Trigonometry Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

[Privacy Policy] [Terms of Use]

© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/