Ângulo x:
->
sen = 1/3
->
cos =
sen² +
cos² = 1
(1/3)²
+ cos² = 1
1/9 +
cos²= 1
cos² =
8/9
cos =
√8/√9
cos =
2√2 / 3
->
senx = 1/3
->
cosx = 2√2 / 3
Ângulo
y:
->
cos = 1/5
->
sen =
sen² + cos² = 1
sen² +
(1/5)² = 1
sen² =
1 - 1/25
sen² =
24/25
sen =
√24 / √25
sen =
2√6 / 5
-> seny = 2√6 / 5
->
cosy = 1/5
cos(x-y)
= cosx.cosy + senx.seny
cos(x-y)
= 1/5 . 2√2 / 3 + 1/3 . 2√6 / 5
cos(x-y)
= 2√2 / 15 + 2√6 / 15
cos(x-y)
= ( 2√2 + 2√6 ) / 15
cos(x-y)
= 2√2.( 1 + √3 ) / 15
