# sin cos

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### sin cos

Why sin^2 + cos^2 = 1 ?

yppetrov

Posts: 9
Joined: Sun Dec 10, 2006 12:19 pm

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

Posts: 5
Joined: Wed Nov 28, 2007 6:12 pm

### Re: sin cos

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 !
dduclam

Posts: 36
Joined: Sat Dec 29, 2007 10:42 am
Location: HUCE-Vietnam

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
anuj94

Posts: 1
Joined: Wed Jul 16, 2008 11:14 pm

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