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[DOC File]Solution of the Diffusion Equation
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Because sin(m x/xmax) is an orthogonal function in the region 0 ≤ x ≤ xmax, the only time that this integral is non zero is when m = 4. We have just shown3 that the integral of sin2(m x/xmax) between x = 0 and x = xmax = xmax/2 so that equation [16] tells us that Cm = 1 when m = 4 and Cm = 0 …
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[DOC File]GCSE A* FOCUS: Transformations of curves
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4) 5) Exam Style Questions: 1) A sketch of the curve y = sin x° for 0 < x < 360 is shown below. (a) Using the sketch above, or otherwise, find the equation of each of the following two curves. (i) (ii) (b) Describe fully the sequence of two transformations that maps the graph of y = sin x° onto the graph of y = 3 sin …
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[DOC File]C3 Trigonometry
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sin x + (3 cos x = 2 sin 2x. (3) (c) Deduce from parts (a) and (b) that sec x + (3 cosec x = 4 can be written in the form sin 2x – sin (x + 60() = 0. (1) 3. (i) (a) Express (12 cos ( – 5 sin in the form R cos (( + (), where R > 0 and 0 < ( < 90(. (4) (b) Hence solve the equation. 12 cos ( – 5 sin ( = 4, for 0 < ( < 90(, giving your answer ...
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[DOC File]January 2005 - 6664 Core C2 - Question paper
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4. (a) Show that the equation. 5 cos2 x = 3(1 + sin x) can be written as. 5 sin2 x + 3 sin x – 2 = 0. (2) (b) Hence solve, for 0 ( x < 360(, the equation. 5 cos2 x = 3(1 + sin x), giving your answers to 1 decimal place where appropriate. (5) 5. f(x) = x3 – 2x2 + ax + b, where a and b are constants. When f(x) is divided by (x …
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[DOC File]Math 111, Review Problems
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(2) Find x and y. (3) Find θ and x. (4) Find α and x. (5) Use the fundamental identities to find the exact value of sin x, csc x, and tan x given that. and . (6) Use a sketch of the unit circle to explain why: a) the function y = sin x is periodic. b) the function y = tan x has the vertical asymptotes where it does
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[DOC File]TRIGONOMETRY
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4) cos (270 - x) 5) sin ( x + ) = 6) cos ( ) Find each of the following numbers: If sin A = , 0 < A < and cos B = , 7) sin (A + B) 8) cos (A – B) 9) tan (A + B ) Algebra 3 Trig Formulas Assignment #6 (1) Find each of the following numbers please. (a) sin(15) (b) cos(15) (c) sin(105) (d) cos(75)
2 x 4 a 0

[DOC File]Name:
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sin x when your angle is entered in radians rather than degrees. (a) Fill in the chart below and then use the values to complete the graph. One row has been done for you. x (radians) x (decimal) y = sin x x (radians) x (decimal) y = sin x 0 5 6 6 0.52 0.5 4 5 4 3 3
y sin x

[DOC File]Volume of Revolution Worksheet
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Disk and Washer Methods (Integrate by hand and double check you work--also practice integrating) 1. Find the volume of the solid of revolution generated by revolving the region bounded by y = 6, y = 0, x = 0, and x = 4 about: (a) the x–axis (452.389) and (b) y–axis (301.593). 2.
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[DOC File]6.2 TRIG FUNCTIONS -- UNIT CIRCLE
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sin t = y/1 = y csc t = 1 / y (y ( 0) cos t = x/1 = x sec t = 1 / x ( x ( 0) tan t = y / x (x ( 0) cot t = x / y (y ( 0) Note: The unit circle is just a special case of this general theorem! Example: A) Find the values of the trig functions corresponding to (-4/5, 3/5) sin θ = csc θ = cos θ = sec θ = tan θ = cot θ =
f x 4 sin x 30

Sin x 0 4