document.write( "Question 250835: find cos θ given that cos2θ = 5/7 and 0≤θ<π/2 \n" ); document.write( "
Algebra.Com's Answer #184443 by drk(1908)![]() ![]() ![]() You can put this solution on YOUR website! Cos2x = cos(x + x) = cosx*cosx -sinx*sinx = cos^2(x) - sin^2(x) \n" ); document.write( "We have the following identity: cos^2(x) + sin^2(x) = 1 ; sin^2(x) = 1 - cos^2(x) \n" ); document.write( "By substitution, \n" ); document.write( "2cos^2(x) - 1 = 5/7 \n" ); document.write( "cos^2(x) = 6/7 \n" ); document.write( "cos(x) = sqrt(6/7) \n" ); document.write( "x = cos^(-1) (6/7) \n" ); document.write( "at this point you put it into your calculator. \n" ); document.write( "x ~ 22.5 degrees, or ~ pi/8.\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |