Question

Найти значение функции в точках:f(x)=0,5sin(x+п/4); x=-п/4; x=п/2; х=0

Answer 1

Ответ:

Пошаговое объяснение:

f(-p/4)=0,5sin(-p/4+p/4)=0,5sin0=0,5*0=0

f(p/2)=0,5sin(p/2+p/4)=0,5sin(3p/4)=0,5*V2/2=1/2*V2/2=V2/4

f(0)=0,5sin(0+p/4)=0,5*V2/2=V2/4

Answer 2

To find the values of the function $f(x) = 0.5 \sin(x + \frac{\pi}{4})$ at the given points $x = -\frac{\pi}{4}$, $x = \frac{\pi}{2}$, and $x = 0$, we simply need to substitute the respective values of $x$ into the function and calculate the results.

1. $x = -\frac{\pi}{4}$: $f\left(-\frac{\pi}{4}\right) = 0.5 \sin\left(-\frac{\pi}{4} + \frac{\pi}{4}\right)$ $f\left(-\frac{\pi}{4}\right) = 0.5 \sin(0)$ Since $\sin(0) = 0$, we have: $f\left(-\frac{\pi}{4}\right) = 0.5 \times 0 = 0$

2. $x = \frac{\pi}{2}$: $f\left(\frac{\pi}{2}\right) = 0.5 \sin\left(\frac{\pi}{2} + \frac{\pi}{4}\right)$ $f\left(\frac{\pi}{2}\right) = 0.5 \sin\left(\frac{3\pi}{4}\right)$ Since $\sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2}$, we have: $f\left(\frac{\pi}{2}\right) = 0.5 \times \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{4}$

3. $x = 0$: $f(0) = 0.5 \sin\left(0 + \frac{\pi}{4}\right)$ $f(0) = 0.5 \sin\left(\frac{\pi}{4}\right)$ Since $\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$, we have: $f(0) = 0.5 \times \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{4}$

So, the values of the function $f(x) = 0.5 \sin(x + \frac{\pi}{4})$ at the given points are: $f\left(-\frac{\pi}{4}\right) = 0$, $f\left(\frac{\pi}{2}\right) = \frac{\sqrt{2}}{4}$