Question

y--1+2 sen x
y= 3 cos x

Answer 1

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