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prove syn(squared)+cos(squared)=1

2007-04-13 13:47:00 · 5 answers · asked by theinen76 2 in Science & Mathematics Mathematics

5 answers

This is true by definition. If you study sins and cosines you will know that it is based on a circle with a radius of 1. The pythagorean theorum says that a^2+ b^2 = c^2 in a right triangle.

2007-04-13 13:56:02 · answer #1 · answered by Nelson_DeVon 7 · 0 0

If you look at a unit circle you will see that any point on that unit circle will have coordinates of (cos(theta),sin(theta)). Since the coordinates are (cos(theta),sin(theta)), a triangle can be drawn with legs of cos(theta) and sin(theta) and with a hypotenuse of the radius (which is 1). Since Pythagoreans theorem is a^2+b^2=c^2 (where a and b are the legs and c is the hypotenuse) we can say

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

which becomes

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


since the radius of the unit circle is 1.

2007-04-13 13:59:11 · answer #2 · answered by Jim 5 · 0 0

soory brother or sis i have never learn this type of question in math

2007-04-13 13:51:10 · answer #3 · answered by Anonymous · 0 1

sin=opp/hyp
cos=adj/hyp

sin^2=opp^2/hyp^2
cos^2=adj^2/hyp^2

sin^2+cos^2=opp^2/hyp^2 +adj^2/hyp^2=(opp^2+adj^2)/hyp^2

by pythagorean theorem, (opp^2+adj^2)=hyp^2 (a^2+b^2=c^2)

so you have hyp^2/hyp^2 which =1

2007-04-13 13:53:59 · answer #4 · answered by Nick 2 · 1 0

awww....man...its soo long ive tooken math....

2007-04-13 13:54:19 · answer #5 · answered by no name 1 · 0 1

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