sin cos

by **yppetrov** » Sat Dec 16, 2006 3:02 am

Why sin^2 + cos^2 = 1 ?

by **babyj** » Mon Dec 03, 2007 6:36 pm

I dont know...i have never seen it like that in my life

by **dduclam** » Sun May 04, 2008 5:10 am

yppetrov wrote:Why sin^2 + cos^2 = 1 ?

Because Pitago theorem show that $a^2+b^2=c^2$

( $0\le \alpha \le90^\circ$ )

Nother value of $\alpha$ ,using trigonometry circle !

by **anuj94** » Wed Jul 16, 2008 11:46 pm

Make a Triangle ABC
In▲ABC take A as a referer and B as 90°
So, AB = Base , BC= Perpendicular and AC = Hypotenous
Sin = P/H = BC/AC
cos = B/H = AB/AC
if AB = ABx , BC = BCx , AC=ACx taking x as a constant
sin^2 + cos^2 = 1
(BCx/ACx)^2 + (ABx/ACx)^2 =1
BC^2 x^2 +AC^2 x^2 + AB^2 x^2 /AC^2 x^2
BC^2 x^2 + AB^2 x^2/AC^2 x^2 =1
cross multiply
BC^2 x^2 + AB^2 x^2=AC^2 x^2
x^2( BC^2 + AB^2 ) = AC^2 x^2
BC^2 + AB^2 = AC^2 x^2/x^2
BC^2 + AB^2 = AC^2
a²+b²=c²
hence proved

sin cos

sin cos

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