Question

Se considera functia f : R -> R, f(x) = sin(2x)
Daca f(a)= 1/3
cat este f(a+pi/2) ?

Answer 1

Răspuns:

$f(a+\frac{\pi}{2}) = -\frac{1}{3}$

Explicație pas cu pas:

$f(a) = \frac{1}{3} \iff \sin{(2a)} = \frac{1}{3}\\ \\ f(a+\frac{\pi}{2}) = \sin{\Big(2\cdot (a+\frac{\pi}{2})\Big)} = \sin{(2a+\pi)} = \sin{2a}\cos{\pi} + \sin{\pi}\cos{2a} = \sin{2a}\cdot (-1) = -\sin{2a}\\ \\ f(a+\frac{\pi}{2}) = -\sin{2a} = -f(a) = \boxed{-\frac{1}{3}}$