SOLUTION: explain the trig identity ((sinx)^2)+((cosx)^2)=1

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Question 656136: explain the trig identity ((sinx)^2)+((cosx)^2)=1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
  • 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:
    a%5E2%2Bb%5E2=c%5E2
  • Divide both sides of the equation by c%5E2:
    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:
    %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:
    %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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