document.write( "Question 1041327: 1. Find csc theta if cot theta = 0.8 when theta is in quad III.
\n" ); document.write( "2. Find cos2theta and sin theta/2 if tan theta=-1/2 and theta is in quad II. \n" ); document.write( "
Algebra.Com's Answer #656374 by Alan3354(69443)\"\" \"About 
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1. Find csc theta if cot theta = 0.8 when theta is in quad III.
\n" ); document.write( "cot = x/y = 4/5
\n" ); document.write( "r = sqrt(x^2 + y^2) = sqrt(41)
\n" ); document.write( "csc = r/y = -sqrt(41)/5 **** negative in Q3\r
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\n" ); document.write( "2. Find cos2theta and sin theta/2 if tan theta=-1/2 and theta is in quad II.
\n" ); document.write( "tan = y/x = -1/2
\n" ); document.write( "r = sqrt(5)
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\n" ); document.write( "sin(t) = y/r = sqrt(5)/5 (+ in Q2)
\n" ); document.write( "cos(t) = x/r = -2sqrt(5)/5 (- in Q2)
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\n" ); document.write( "cos(2t) = 2cos^2(t) - 1 = -0.2
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\n" ); document.write( "sin^2(t) = (1 - cos(t))/2 = (1 + 2sqrt(5)/5)/2 = 1/2 + sqrt(5)/5 = (5 + 2sqrt(5))/10
\n" ); document.write( "\"sin%28t%2F2%29+=+sqrt%28%285+%2B+2sqrt%285%29%29%2F10%29\"\r
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