document.write( "Question 753010: use the pythagorean identity to find cos theta when sin theta equals 60 divided by 61 and theta is in the second quadrant \n" ); document.write( "
Algebra.Com's Answer #458179 by DrBeeee(684)\"\" \"About 
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The identity you refer to is
\n" ); document.write( "(1) sin^2(theta) + cos^2(theta) = 1, independent of the quadrant in which theta lies. Using the value of sin(theta) we get
\n" ); document.write( "(2) (60/61)^2 + cos^2(theta) = 1 or
\n" ); document.write( "(3) cos^2(theta) = 1 - (60/61)^2 or
\n" ); document.write( "(4) cos^2(theta) = (61^2 - 60^2)/(61)^2.
\n" ); document.write( "The numerator of the right side of (4) is the difference of two perfect squares, therefore can be factored into the product of the sum and difference or
\n" ); document.write( "(5) cos^2(theta) = [(61-60)*(61+60)]/(61)^2 or
\n" ); document.write( "(6) cos^2(theta) = (1*121)/(61)^2 or
\n" ); document.write( "(7) cos^2(theta) = (11)^2/(61)^2 or taking the square root of both sides we get
\n" ); document.write( "(8) cos(theta) = +/- 11/61.
\n" ); document.write( "Since theta is in the second quadrant we select the negative value of the cosine and we get
\n" ); document.write( "(9) cos(theta) = -11/61
\n" ); document.write( "Answer: the cos(theta) = -11/61
\n" ); document.write( "Look Mom, \"no calculator\".
\n" ); document.write( "By the way we can check our answer using (1).
\n" ); document.write( "Is ((60/61)^2 + (-11/61)^2 = 1)?
\n" ); document.write( "Is (3600/3721 + 121/3721 = 1)?
\n" ); document.write( "Is (3721/3721 = 1)?
\n" ); document.write( "Is (1 = 1)? Yes \n" ); document.write( "
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