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Wave Equation : Triangular Pulse

Let u(x; y) be the solution on 0 < x < 2 and 0 < y < 2 of uxx + uyy = 0 with u(0, y) = u(2, y) = u(x, 2) = 0 and u(x, 0) = f(x) the triangular pulse with f(0) = f(2) = 0 and f(1) = 2. f(x) = {2x 0<x<1 {-2x+4 1<x<2 Let uj,k = u(j/2; k/2) for j = 1; 2; 3 and k = 1; 2; 3 as obtained by the numerical method. (a)

Trigonometric Substitution

Please see the attached file for the fully formatted problem. Use trigonometric substitution to write the algebraic expression sqrt(36-4x2) as a trigonometric function, where the substitution is x = 3 cos theta and 0<theta<pi/2.

Trigonometric equation

See attached file --- find all solutions of the equation in the interval [0,2&#61552;). tan(x+ pi) + 2sin(x+pi) = 0 [show all the steps in solving this equation, not just the answer] ---

10 Trigonometry Application Word Problems : Angles and Lengths

1. Suppose that a boat leaves Jacksonville traveling at a bearing of 110o. It goes 30.0 km, and then travels 100.0 km at a bearing of 170o. How far is it from Jacksonville? 2. Suppose that I am trying to judge the distance across a lake. I stand facing some house on the opposite shore. I turn 95o to the left, and walk 20 me

Half and quarter range sine and cosine expansion

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. 6. In each case solve (1) with boundary conditions (1b) changed as indicated, and for the specified f(x). Use a half- or quarter-range cosine or sine expansion, as appropriate... Please see attached.

Solving Trigonometric Equations

Solve each equation for exact solutions in the interval [0, 360]. Use either an algebraic method or a graphical method. 2 sin x -1 = csc x

Proving Trigonometric Identities

Prove sec 2A + tan 2A = (cos A + sin A)/ (cos A - sin A) Express this as a sum of 2 trigo functions 2(siny)(sin5y) Prove (sin2A)^2 - (sinA)^2 = (sinA)(sin3A)

Related Rates and Trigonometry : Rate of Rotation of a Searchlight

A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight?


There are 3 problems. The first and second problem are with the dotted lines both are division problems. I am looking for the expression for each. 1) Sin(x + B) + cos( x - B) --------------------------- = Cos(x + B) - sin(x - B) 2.) Tan2x + sin2x = -----------------

Trigonometric Expression

1) 2 tan (theta /2)= 2) 2 tan theta Sin ^2 (theta /2)= 3) 2 Cos (45 + x) Cos (45-x)= 4) (Sin 3 x - 3 Sin x )/ ( Cos 3 x + 3 Cos x) = 5) 2 tan (theta /2) / { 1 + tan ^2 (theta /2) } = 6) Find the least positive value of theta such that tan (45+ theta ) - 3 tan theta =2

Trigonometric Identities

I have a attachment of 2 problems of which I am trying to solve. For both of these problem, I am to derive an expression. Derive a Trigonometric expression. Please see attached.

Solve Trigonometric Equations

Solve for x: sin x = cos x Solve for x: cos x - 6 sec x = 1 Both are 0 is less than or equal to x and x is less than or equal to 2 Pi

Trigonometry and nautical miles

Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N(e) = 6066 - 31 * cosine 2e. e represents the latitude in

Right angle trigonometry

A V-gauge is used to find the diameters of pipes. Look at the figure in the attachment, the measure of angle AVB is 54°. A pipe is placed in the V-shaped slot and the distance VP is used to predict the diameter. a. Suppose that the diameter of a pipe is 2 cm. What is the distance VP? b. Suppose that the distance VP is 3.9