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3) Given the following list of possible trig identities, state which ones are true. If some are true only on a finite domain, state what the domain is that allows the trig identity to be true. sin (x) = sec- (y) = sec(y2) sin (-x ) = -sin (x+ 7 ) = sin (x+2x) sin(x) arctan(tan( y)) = y csc' (x) = [csc(x)] tan x tan x sin(csc-1 x) =?1 X arctan(x) = tan(x)-1 sin (sin ( x) ) =' sin?(x) cos(cos x) = x sin (xy) ='sin* (xy) tan (x X tan ( x ) 4 tan(x) = tan(4x) sin (-x) =' -sin (x) sinsin (x) ) = sin (sin-' (x))1.3 Find the absolute magnitude of each complex number and write it in polar form, z = I R| exp(if). Give your answer in terms of explicit values for 0. For example, i = exp(in /2). r and y are real variables. (a) : (b) It: (c) r tiy. 1.4 (6 points) First-order differential equations. Plutonium is very lethal to humans, even in small doses. Its half life is 24,100 years. Once ingested, it takes 200 years before the amount ingested decreases by a factor of two. If the expected lethal dose is r, and a patient has inhaled a dose y, find the formula for the time required to clear the original dose to a safe level.Let S be a basic solid and let (a, b, c) be a point not in S. If S has continuously varying mass density o = 6(x, y, z) then S attracts a point mass m located at (a, b, c) with a gravitational force F = Gmo(z, y, 2) f(x, y, 2 ) dx dy de, S where f(x, y, 2) = (x - a)i + (y - b)j + (2 - c)k [(x - a)2 + (y - b)3 + (2 - c)213/2 is the force experienced by a particle in an inverse square field. Let S be a solid right circular cylinder of constant density, with base radius R, height h and mass M. A point mass m is placed on the axis of S at a distance o from the nearest base of the cylinder. Find the gravitational force exerted by the cylinder on the point mass. Hint: In developing the integral for F you might like to consider only the non-zero components due to the geometrical symmetry of the