1
$\begingroup$

I've been solving some problems on signals for practice and I solved a particular one in two ways. The first way gave me this result : $$V(t)=\frac{2}{π}(\sin t+\cos t)$$

The second way gave: $$V(t)=\frac{4}{π\sqrt2}\sin\left(t+\frac{\pi}{4}\right)$$

Plotting this two online they seem to be the same. How can I prove this mathematically? I haven't used trigonometric formulas much so I don't have many ideas. I tried turning the sint to a cosine and then applying the addition formula of cosa+cosb but that doesn't help.

$\endgroup$
2
$\begingroup$

HINT

Recall that

$$\sin (t+\pi/4)=\sin t\cos (\pi/4)+\cos t\sin (\pi/4)$$

$\endgroup$
0
$\begingroup$

Hint 1:$$$$$2$ functions $f(x)$ and $g(x)$ are considered equal if and only if they have the same domain $D$, and the same value of $f(x)$ and $g(x)$ for any $x\in D$. $$$$ Hint 2:$$$$ $V_1(t)=\frac{2}{π}(\sin t+\cos t)$ and $V_2(t)=\frac{4}{π\sqrt2}\sin(t+π/4)$ have the same domain ($R$ - the set of Real Numbers). $$$$ Hint 3: $$$$ $$V_1(t)=\frac{2}{π}(\sin t+\cos t)=\dfrac{2\sqrt 2}{\pi}\left(\dfrac{\sin t}{\sqrt 2}+\dfrac{\cos t}{\sqrt 2}\right)=\frac{4}{π\sqrt2}sin(t+π/4)=V_2(t)$$ $$$$ Note that $\sin (t+\pi/4)=\sin t\cos(\pi/4)+\sin(\pi/4)\cos t$

$\endgroup$
  • $\begingroup$ Why must you use 3 empty lines? Also, use \sin x instead of sin x for LaTeX formatting. $\endgroup$ – Andrew Li May 21 '18 at 7:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.