document.write( "Question 691180: The following problems give an expression for one of the three functions sin , cos, or tan ,with (theta) in the fi rst quadrant. Find expressions for the other two functions. Your answers will be algebraic expressions of x.
\n" ); document.write( "(a) sin  = 3=x
\n" ); document.write( "(b) x = 4 cos 
\n" ); document.write( "(c) tan  = x \n" ); document.write( "
Algebra.Com's Answer #426538 by stanbon(75887)\"\" \"About 
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The following problems give an expression for one of the three functions sin , cos, or tan ,with (theta) in the fi rst quadrant. Find expressions for the other two functions. Your answers will be algebraic expressions of x.
\n" ); document.write( "(a) sin  = 3/x
\n" ); document.write( " Since sin = opp/hyp, opp = 3 and hyp = x
\n" ); document.write( "Then adj = sqrt[x^2-3^2] = sqrt[x^2-9]
\n" ); document.write( "cos = sqrt(x^2-9)/x
\n" ); document.write( "tan = (3/x)/[(x^2-9)]/x] = 3/(x^2-9)
\n" ); document.write( "---------------------------------------
\n" ); document.write( "(b) x = 4 cos
\n" ); document.write( "cos = x/4
\n" ); document.write( "Since cos = adj/hyp, adj = x and hyp = 4
\n" ); document.write( "Then opp = sqrt[4^2-x^2]
\n" ); document.write( "---
\n" ); document.write( "sin = opp/hyp = sqrt(16-x^2)/4
\n" ); document.write( "tan = opp/adj = sqrt(16-x^2)/x
\n" ); document.write( "====================================== 
\n" ); document.write( "(c) tan  = x/1
\n" ); document.write( "Since tan = opp/adj, opp = x and adj = 1
\n" ); document.write( "---
\n" ); document.write( "Then hyp = sqrt(x^2+1]
\n" ); document.write( "sin = x/sqrt(x^2+1)
\n" ); document.write( "cos = 1/sqrt(x^2+1)
\n" ); document.write( "===========================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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