Explore BrainMass

Explore BrainMass

    Trigonometry

    BrainMass Solutions Available for Instant Download

    15 Trigonometry Problems : Angular Velocity, Shadows, Waves and Triangles

    Trigonometry Review 1. Assume the angle of inclination of the sun is given by Theta = (pi/12)t, where t is the number of hours after sunrise. Suppose we have a 10 meter high flagpole. a. What is the angular velocity of the sun? b. Write an equation for the length of the flagpole's shadow when the angle of the sun is theta rad

    one-dimensional wave equation for a semi-infinite string

    Find the solution to: PDE: u*xx-c(to the power of negative k)u*tt=0 , 0 ICs: u(x,0)=f(x) and u*t(x,0)=g(x), x>=0 BC: u*x(0,t)=0 , t>=0 This BC corresponds to a string with its end point free to move in a vertical direction. (Please remember to include to boundary condition in your solution. Thanks very much!)

    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)

    Angle Conversions and Trigonometric Functions

    See the attached file. 1. Convert the measure to radians : 2/3 revolution counterclockwise from the x-axis. 2. Evaluate arcsin ½. 3. Evaluate csc(arcsin5/13). 4. Evaluate sin(artan pi). [Please show your steps]. Please see the attached file for the fully formatted problems.

    Use the sum and difference formulas to find the exact value

    Use the sum and difference formulas to find the exact value of cos(255 degrees) Which of these is the correct answer? A. (-&#8730;2 + &#8730;6)/4 B. (&#8730;2 - &#8730;6)/4 C. (&#8730;2 + &#8730;6)/4 D. (-&#8730;2 - &#8730;6)/4 [show your steps in completing this problem]

    Trigonometric Substitution: Write an Algebraic Expression

    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 Intervals

    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] ---

    Vibrating String and d'Alembert's Solution in Wave Equation

    2. Show that, like the wave equation, the given PDE is hyperbolic and find its general solution by introducing the suggested change of variables. (b) uxx - 4uxy - 5uyy = 0 ........ Please see the attached file for the fully formatted problems.

    Separation of Variables: Vibrating Membrane in Wave Equation

    1. Obtain the solution to the initial-value problem (1) for the given f(x, y), a, and b, and give the relations that define the nodal lines of w, if any. Let c=1 in each case. (e) f(x, y) = 1.05 sin 3x sin y - sin x sin 3y, a = pi, b = 2pi. See the attached file.

    10 Trigonometry Application Word Problems: Angles and Lengths

    See the attached file. 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

    Half- and quarter-range sine and cosine

    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.

    Even and Odd Function

    5. Determine fe(x) and fo(x). Is f even? Odd? Neither? - See attachment. (g) x^4 + x^3 + x^2 + x + 1 (j) sin(sin x) (k) cos(sin x) (^ is raised to the power of) fe(x) means even function. fo(x) means odd function.

    Identities of Plane Trigonometry

    Important Formulas and their Explanations (VI): Identities of Plane Trigonometry Pythagorean Relation Pythagorean Identities Pythagorean Identities

    Related Rates & 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? See the attached file.

    Trigonometric Expression Problems

    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 = -----------------