Circular Functions & Trig

Sep 2008
114
0


With this second one, I understand why sine x cannot equal 0 but I do not understand/have no idea what kpi is


 

Grandad

MHF Hall of Honor
Dec 2008
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Hello juliak

The comments in red are correct: it should read
\(\displaystyle \tan\theta =\pm\tfrac12\)
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?

Grandad
 
Sep 2008
114
0
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?

Grandad

 

Grandad

MHF Hall of Honor
Dec 2008
2,570
1,416
South Coast of England
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?

Grandad