Imagine a trigonometric circle with radius equal to 1.
We can say that the opposite side of the angle generated by the origin is equal to sen Ф and the adjacent equal to cos Ф
With this we can say that:
h² = c² + c²
If r = 1, then h = 1
1² = cos² + sen²
1 = cos² Ф + sen² Ф
You can use this equation a lot of times because it's the fundamental trigonometric relation
, so, when you something like:
sen Ф = cos Ф + 1
you can take from sen² Ф + cos² Ф = 1 that [tex]sen = \sqrt{1 - cos^2}[/tex] and then resolve.
Suppose we have a right- angled triangle with theta has one of the angles ( not 90 degrees) and hypotenuse c , opposite side a and adjacent side b.
then sin α = a/c giving a = c sin α .............(1)
and cos α = b/c giving b = c cos α...............(2)
by Pythagoras theorem:-
a^2 + b^2 = c^2 and from equations (1) and (2):-
a^2 + b^2 = c^2 sin^2 α + c^2 cos^2 α
a^2 + b^2 = c^2 ( sin^2 α + cos^2 α)
Comparing this equation with the Pythagoras equation sin^2 α + cos^2 α must equal 1.
