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Pythagorean Triples and Quadratic Coefficients

1. If a + b = 7, and a2 + b2 = 37, then what is the value of ab? 2. Isn't there an easy way to find out Pythagorean Triplets? 3:4:5 6:8:10 5:12:13 8:15:17 7:24:25 Please provide an equation or easy way to get triplets- e.g. some kind of relation. See the attached file.

Simplify Trig Functions

Simplify: tan (2 arc cos (x/3)) Solution shall not contain trig and inverse trig functions. Do not use calculator.

Solve Trigonometric Expressions (Arcsin and Arccos)

Set -pi/2 <= x <= pi x = arcsin[sin(5pi/3)] = _______pi x = arcsin[sin(7pi/4)] = _______pi x = arccos[cos(-5pi/6)] = ______pi x = arccos[cos(3pi/2)] = _______pi x = arccos[cos(3pi/4)] = ______pi x = arctan[cos(3pi/2)] = ______pi x = arcsin[sin(7pi/6)] = _____pi Write as a multiple of pi. pi = 3.14159.

Given a space curve C defined

Given a space curve C defined by r(t)=(3 sin t)I + (3 cos t)j + 4tk. Find v(t), a(t), T(t), K, N(t), B(t), aT and aN at t=pi/2. ---

Solution to the following trigonometry questions

A) looking for the distance VP b) diameter of the pipe c) formula for d in terms of VP d) formula for VP in terms of d ----------------------------------------- 1) tire durability 2) tan(x+450 degrees0 cannot be simplified using tangent sum formula. why? 3) difference between trig equation that is an identity and trig equ

Review of previous posting

(See attached file for full problem description and diagrams) --- Need help with the following questions. A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high.

Trigonometry: Close Encounters of the Third Kind

In the movie Close Encounters of Third Kind, there was a scene where the star, Richard Dreyfuss, was approaching Devil's Tower in Wyoming. He could have determined his distance from Devil's Tower by first stopping at point P, and taken a measurement of the angle from his location to the height of the tower of 13.5 degrees. He


--- (See attached file for full problem description)

Spherical Polar Coordinates

I am trying to find the grad function of the spherical polar coordinates shown on the attached file. I have completed the question to a certain extent but am not sure if it is correct. Could you please ensure its accuracy and complete by simplifying the solution (trig identities etc) as I am unable to do so? (See attached f


What is the difference between a trig equation that is an identity and a trig equation that is not an identity? Provide an example to clarify.

Tangent sum formulas

Explain why tan(x + 450 degrees) cannot be simplified using the tangent sum formulas but can be simplified by using the sine and cosine formulas. (Please show all work).

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] ---