# What is one negative figure written in Pi/radian notation for y=sin4x

So with $$y = \sin (4x)$$ I divide $$4$$ by $$2\pi$$. All youtube tutorials show $$-1$$ is obtained by doing $$\sin(3 \pi /8)$$

I've tried this in a calculator with the mode set to radians, but no matter what variation, I can not get a negative value to appear.

What $$x$$ will get to $$-1$$?

Since $$\sin\left(\frac{3\pi}{2}\right) = -1$$, then $$4x = \frac{3\pi}{2} \implies x = \frac{3\pi}{8}$$ will work to have $$y = \sin(4x) = -1$$.
The problem with checking $$\sin\left(\frac{3\pi}{8}\right) = \sqrt{\frac{1}{2}\left(1 + \frac{1}{\sqrt{2}}\right)} \approx 0.924$$ is that it's $$x = \frac{3\pi}{8}$$, with $$4x = \frac{3\pi}{2}$$ being the argument to $$\sin$$, to get a result of $$\sin(4x) = -1$$.
• @Anon You're welcome. I don't understand what you mean by $\sin 4x = 2\pi / 4 x 4$. Note $\sin(4x)$ means to take any $x$, multiply it by $4$ & then apply the $\sin$ function to it. As for using the $4$ inside the $\sin$ function, if it helps any, consider it to be $y = 4x$ and $\sin(y)$ instead. As for $4$ being "used up to make 3pi/8", the key element is that for the result of $\sin$ to be $-1$, the input needs to be $\frac{3\pi}{2} + 2k\pi$, but we use $k = 0$ here. As the input is $4x$, for it to be $\frac{3\pi}{2}$ means $x = \frac{1}{4}\left(\frac{3\pi}{2}\right) = \frac{3\pi}{8}$. – John Omielan Jan 24 at 5:08