how do you prove that sin^2 (x) + cos^2(x) = 1 ?

Question

how do you prove that sin^2 (x) + cos^2(x) = 1 ?
please give an example

Answer 1

opp = opposite side

adj = adjacent side

hyp = hypotenuse
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sin x = opp / hyp

cos x = adj / opp
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Use Pythagorean Theorem

adj^2 + opp^2 = hyp^2

Divide by hyp^2

adj^2 / hyp^2 + opp^2 / hyp^2 = 1

adj / hyp = cos x

adj^2 / hyp^2 = cos^2 x

opp / hyp = sin x

opp^2 / hyp^2 = sin^2 x

cos^2 x + sin^2 x = 1
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Happy Halloween!

Answer 2

The gist of the solution is what sine and cosine represent. Sine and Cosine represent the x and y coordinates of a unit circle (i.e. a circle with radius 1). A triangle generated by such coordinates yields a hypotenuse of 1, so that

sin^2(x) + cos^2(x) = 1^2

OR

sin^2(x) + cos^2(x) = 1

That's a bit of an informal proof right there.

Answer 3

Draw a right triangle and have legs a, b and Hypo c

sin x = a/c and cos x = b/c

so sin^2(x) + cos^2(x) = (a/c)^2 + (b/c)^2 = (a^2 + b^2)/c^2
= c^2/c^2 = 1

Answer 4

Start by noticing sinx = cos(x - pi/2). Start with that square plus cosx squared and use the cos(A+B) equations. It falls right out after that.

Answer 5

cos(50)^2 = .413175

sin(50)^2 = .586824

.413175 + .586824 = .999999 (which is 1 considering I had or round the other decimals)

Answer 6

good question let me know when you workout the problem then again let me know the grade you make :)