MAT137Y1 Lecture : MAT 137Y 2007-08Winter Session, Self Generated Solutions to Problem Set 2.pdf
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MAT137Y1 Full Course Notes
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Mat 137y 2007-08 winter session, solutions to problem set 2. 1 (she section 1. 6: it is known that sinx has period 2 , so sinax has period 2 /a. Therefore sin 1: g( x) = sec( x) = 1, we use the gure below. h = csina and x = ccosa. 2x has period 4 . cosx = secx = g(x) (since cosx is even). Therefore g is also even. cos( x) = 1 a2 = h2 + (b x)2 = c2 sin2 a + b2 2bccosa + c2 cos2 a = b2 + c2 2bccosa. 2 (a) notice that k sin(x + ) = k sinxcos + k cosxsin . Therefore k sinxcos + k cosxsin = asinx + bcosx = a = k cos , b = k sin . Observe that a2 + b2 = k2 cos2 + k2 sin2 = k2. Hence, k =(cid:112)a2 + b2, (b) for (i), we have a = 1 .
