document.write( "Question 656136: explain the trig identity ((sinx)^2)+((cosx)^2)=1
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Algebra.Com's Answer #409584 by jsmallt9(3758)\"\" \"About 
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  • Draw a right triangle and label one of the acute angles as \"x\".
  • Label the side opposite to x as \"a\", the side adjacent to x as \"b\" and the hypotenuse as \"c\".
  • From the Pythagorean Theorem we know that:
    \n" ); document.write( "\"a%5E2%2Bb%5E2=c%5E2\"
  • Divide both sides of the equation by \"c%5E2\":
    \n" ); document.write( "\"a%5E2%2Fc%5E2%2Bb%5E2%2Fc%5E2=c%5E2%2Fc%5E2\"
  • The right side simplifies to a 1 and we can use a property of exponents to rewrite the terms on the left side:
    \n" ); document.write( "\"%28a%2Fc%29%5E2%2B%28b%2Fc%29%5E2=+1\"
  • Looking at the triangle we should be able to see that a/c = sin(x) and b/c = cos(x). Substituting these into our equation we get:
    \n" ); document.write( "\"%28sin%28x%29%29%5E2%2B%28cos%28x%29%29%5E2=1\"
  • So the identity is simply the Pythagorean equation expressed in terms of Trig functions!
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