Ask Dr. Math High School Archive

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 TOPICS This page:   trigonometry    Search   Dr. Math See also the Dr. Math FAQ:   trigonometry formulas See also the Internet Library:   trigonometry HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Trigonometry Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     DeMoivre's theorem.     Volume of a tank. Trigonometry by Hand [05/24/2002] What formulas can I use to compute sines, cosines, tangents, arcsines, arccosines, and arctangents without using tables or a calculator? Trigonometry Equations [04/23/2003] Solve, for 0 <= theta < 360, 3cos^2(theta) - 2sin(theta) = 2, giving solutions to 1 decimal place where appropriate. Trigonometry + Geometry [5/5/1996] A right angle triangle is blocking a circle and is being blocked by another circle... Trigonometry Identities [01/07/1997] Verify the identity sin(x+y+z) = sinx cosy coxz + cosx siny cosz + cosx cosy sinz - sinx siny sinz. Trigonometry Identities [07/30/1997] I have a problem with these identities... Trigonometry Identity [02/20/1998] Prove a*cos(A) + b*cos(B) + c*cos(C) = 4R*sin(A)*sin(B)*sin(C). Trigonometry, Logs and Map Projections [10/01/1997] I am trying to figure out the inverse function used by the Mercator map projection. Trigonometry Mnemonic [04/12/1997] How do you spell the trigonometry word that is something like SOCHOATOA? It means side over hypotenuse, etc. Trigonometry Problem [8/11/1995] A 12 metre ladder is inclined to the vertical at 48 degrees. How far is it from the base? Trigonometry Proof [6/20/1996] Prove that if a,b,y > 0 and a+b+y = pi, then sin(2a)+sin(2b)+sin(2y) = 4(sin a)(sin b)(sin y) Trigonometry Proof [7/18/1996] How do I prove that (cotX)(cosX)/(cotX + cosX) = (cosX)/(1 + sinX)? Trigonometry Proof [04/21/1997] Prove that (sin 50 x cos 50)/tan 50 = sin^2 40. Trigonometry Story Problem [06/04/2002] What angle will a shortcut make with the roads nearest it? Trigonometry Substitutions [09/30/1997] I am having problems doing trig substitutions. Can you suggest any methods? Trigonometry Terminology [10/24/2001] Why is the term 'arc' used for the inverse of sine, cosine, and tangent, instead of just saying the function to the -1 power? Trigonometry Tricks [11/14/2002] To find how (1/4)cos^4x-(1/6)cos^6x = -(1/4)sin^4x+(1/6)sin^6x, I've tried to change all the cos to sin by using sin^2x+cos^2x = 1 and then using double angle formulas. I am trying to prove that they are equal to each other. Trigonometry Without Calculators [01/06/1997] How do you find Cos[40] without a calculator? Trigonometry Word Problem [06/05/2002] How far did the hot-air balloon rise between observations? Trig Problems [05/07/1999] What are the steps to follow in order to answer these questions? 1) cos2x = sinx; 2) cos2x = cosx... Trig Problem: Sec A = -2 ... [10/20/1997] How can I find all the angles in the range between 0 and 2*pi radians that have a secant equal to -2? Trig Proof - Newton's Formula [04/09/1998] Can you prove that: (a - b)/c = sin ((1/2)(A - B))/cos ((1/2)(C))? Trig Proof: Two Methods [03/26/1998] Prove: (1 + sin x + cos x)/(1 - sin x + cos x) = (1 + sin x)/cos x. Trig Ratios of a Right Angle in a Right Triangle [09/21/2006] I'm learning about trig ratios in terms of the hypotenuse, opposite, and adjacent sides of a right triangle. I'm wondering how those sides apply to the right angle? Is the hypotenuse the opposite? What's the adjacent? Trig Word Problem [5/5/1996] Find the height of the tower... Trisected Hypotenuse of a Triangle [12/20/1998] In right triangle ABC, with C as the right angle... what is the length of AB (the hypotenuse)? The Troublesome Endpoints of a Trigonometric Series [04/10/2011] A student has doubts about the radius of convergence assumed in a proof that involves integrating a power series. Doctor Vogler confirms his suspicion about the behavior of endpoints of integrated series, and introduces Abel's Theorem. Tutorial material/books/help [11/16/1998] Can you suggest something I can order or download to help me with trigonometry and pre-calculus? Two Airplanes [08/28/1997] Draw a diagram using coordinate system with origin O - how far apart are the airplanes? Express the answer in radical form. Two Dogs Pulling a Sled [10/15/2001] What are the magnitude and direction of the force the person will have to exert on the sled to keep it moving along the centerline of the road at constant velocity? Two Problems on Tangents [07/09/1998] How can you show that the arc and the angle formed by two tangents are supplementary? Find the radius of circle O, given the following... Two Slopes, and Two Ways to Average Them [01/06/2016] An adult has questions about the validity of a colleague's simple method to average slopes — and about simplifying his own, more involved approach. With sketches, trigonometric identities, and conjugate products, Doctor Peterson explains the methods, and shows their equivalence. Two Triangle Problems [6/11/1996] One angle of a triangle is trisected... Find the shortest side. Two Trigonometry Questions [1/22/1995] What is sin60 * cos60, and tan45 * tan3? Understanding Bearings in Directional Problems [01/14/2004] A boat sails 10km from a harbor H on a bearing of S30 degree E. It then sails 15 km on a bearing of N20 degree E. How far is the boat from H? What is the bearing from H? Unit Sphere [01/21/2002] Is there such thing as a "unit sphere" that has to do with trigonometric functions and the placement of points on said sphere? Usefulness of De Moivre's Theorem [2/10/1996] What is the usefulness of de Moivre's theorem? Using Forth to Find asin(x) or acos(x) [03/16/2004] I am writing a program in Forth. I have available tan, atan, cos and sin. I have three sides of an oblique triangle. How can I find the angles? I know I can do it if I have asin. Is there another way, or can I define asin in terms of what I have available? Using Graphs of Trigonometric Functions [10/9/1995] We are working on csc, sec, and cot graphs, including how to change the sin, cos, and tan graphs to get them. I am interested in applications of these graphs. In what field would it be useful to know the period, the location of the asymptotes, and the domain of a sec graph? Using Newton's Method to Solve an Implicit Equation [10/14/2007] How can I solve the equation (sin(X))/X = 0.7031? My book gives the answer but does not explain how to find it. Using Phase Shifts to Modify a Sine Curve [06/30/2005] What modifiers can be used to fatten a sine wave while not affecting the zeros and peaks? Page: []

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