I'm making some math exercises (not homework, out of interest). Given is the following graph:
I have to determine which funtion $y(x)$ is shown.
Possibilities:
A: $y=3*sin(\frac{\pi}{2}*x+\frac{\pi}{2})$
B: $y=1.5*sin(\frac{\pi}{2}*x+\pi)$
C: $y=1.5*sin(8*\pi*x+\pi)$
I know that the answer should be B, but I don't know how to get there. Could anyone give me a hint on how to approach this, or where to find a good explanation of similar problems online?
Thanks!
If you have an equation of the form $y = A \sin( \frac{2 \pi}{p}(x + b))$ then, it will have an amplitude of A, a period of length $p$, and be translated to the left by $b$. Therefore, for your wave, notice it has amplitude 1.5, and must be $B$ or $C$. Then, notice it has period 4, so, we can re-write $\frac{\pi x}{2} = \frac{2 \pi x}{4}$, and we see that $B$ fits the criteria, while $C$ does not.
It also happens that if this wasn't process of elimination, you recall the $\sin(0) = 0$ but is increasing at $0$. However, $\sin(\pi) = 0$ and $\sin(x)$ is decreasing at $x=\pi$. That's why we have a $b = \pi$. Moreover, your answer could be $\sin( \frac{\pi x }{2} + (2k+1) \pi)$ for any $k \in \mathbb{Z}$.