# Circular Functions & Trig

#### juliak With this second one, I understand why sine x cannot equal 0 but I do not understand/have no idea what kpi is  MHF Hall of Honor
Hello juliak

$$\displaystyle \tan\theta =\pm\tfrac12$$
But I don't know what you mean by
With this second one, I understand why sine x cannot equal 0
Is there any suggestion that $$\displaystyle \sin x$$ is equal to $$\displaystyle 0$$?

Also
but I do not understand/have no idea what kpi is
I don't know what kpi stands for either. Where does it appear anyway?

#### juliak

Hello juliak

But I don't know what you mean byIs there any suggestion that $$\displaystyle \sin x$$ is equal to $$\displaystyle 0$$?

AlsoI don't know what kpi stands for either. Where does it appear anyway? MHF Hall of Honor
Hello juliak OK. I now know what kpi is: $$\displaystyle k \pi$$. But I still don't see where $$\displaystyle \sin x \ne 0$$ is relevant in your original post.

However, what you have written here is easy to understand. If $$\displaystyle \sin x \ne 0$$, then $$\displaystyle x$$ cannot be a multiple of $$\displaystyle \pi$$. (Since the sine of all multiples of $$\displaystyle \pi$$ is zero.) In other words:
$$\displaystyle \sin x \ne 0$$

$$\displaystyle \Rightarrow x \ne k\pi$$, where $$\displaystyle k$$ is an integer

$$\displaystyle \Rightarrow x \ne 0 + k\pi$$
Have we cleared all this up now?