# Thread: Periodic function - find the first positive three values of x...

1. ## Periodic function - find the first positive three values of x...

f(x)=4sin[(pi/2)x]+2

Find the first three positive values of x for wich f(x)=5.

I was able to get one of the answers(0.54) and another on by adding the period (4+0.54=4.54), but i couldnt get the one in between.

2. Hello, JOhkonut!

$\displaystyle f(x)\:=\:4\sin\left(\frac{\pi}{2}x\right) +2$

Find the first three positive values of $\displaystyle x$ for which $\displaystyle f(x)\:=\:5$

Solve for $\displaystyle x\!:\;\;4\sin\left(\frac{\pi}{2}x\right) +2 \;=\;5\quad\Rightarrow\quad \sin\left(\frac{\pi}{2}x\right) \:=\:\frac{3}{4}$

. . . . $\displaystyle \frac{\pi}{2}x \:=\:\arcsin(0.75)\quad\Rightarrow\quad x \;=\;\frac{2}{\pi}\arcsin(0.75)$ .[1]

$\displaystyle \text{Let }\theta_1 \:=\:\arcsin(0.75) \:=\:0.84806$

. . Then: .$\displaystyle \theta_2\:=\:\pi-\theta_1,\;\;\theta_3\:=\:\theta_1 + 2\pi$

Substitute these into [1].