Concerning equivalence of sini (sinus pl.(?))

[Master replies:]

If sin(x)=sin(x') ,where x is some angle and x' a angle of another triangle, does it then follow that sin(x-90°)=sin(x'-90°)=cos(x)=cos(x')?

 

[Master replies:]

More generally if the sinus of a angle is equivalent to another does that mean the angles are the same?

 

[SteamKing]

More generally if the sinus of a angle is equivalent to another does that mean the angles are the same?

Not necessarily. There are identities covering for which angles the sine (and all the other trig functions) has the same value. If you don't want to look these up, you can draw the graph of y = sin (x) and pick them out (remember, sine is a periodic function).

BTW, the plural of "sine" is "sines" in English.

 

[Master replies:]

So is this true: sin(x)=sin(x')→sin(90°-x)=sin(90°-x')=cos(x)=cos(x')?

 

[SteamKing]

So is this true: sin(x)=sin(x')→sin(90°-x)=sin(90°-x')=cos(x)=cos(x')?

Like I said, you can look up the trig identities spelling out the details.

Google "trig identities"

 

[Master replies:]

I don't quite understand what you mean. If all I know is that sin(x)=sin(x') is it then also true that sin(90-x)=sin(90°-x'). I am sure it is. Do sines only differ by angle, as they only depend on the angle? Sorry if I repeat myself.

 

[SteamKing]

I don't quite understand what you mean. If all I know is that sin(x)=sin(x') is it then also true that sin(90-x)=sin(90°-x'). I am sure it is. Do sines only differ by angle, as they only depend on the angle? Sorry if I repeat myself.

It's very simple. Trig identities can be found on the web by looking them up in a search engine, as I have already stated. You are using a computer to communicate with PF, so you can use the search engine to find these trig identities as easily as I can ...

 

[Master replies:]

No I mean i don't understand what the trig identities have to do with my problem?

 

[Mark44]

No I mean i don't understand what the trig identities have to do with my problem?

All of the trig functions are periodic, which means that two different angles can have the same sine (or cosine, tangent, etc.).

This can be seen by looking at a graph of any of these functions. The trig identities mentioned several times by SteamKing provide formulas such as $\sin(x + 2\pi) = \sin(x)$ and many others. As advised, make a web search for trig identities.

 

[Master replies:]

But only the angles in that only differ by a multiple of pi they are not compltly different.

 

[Mark44]

But only the angles in that only differ by a multiple of pi they are not compltly different.

What you wrote is unintelligible. The period for some of the trig functions is $2\pi$, so, for example, $\sin(x + \pi) \ne \sin(x)$.

they are not compltly different.

What are not completely different?

 

[mathman]

For 0 < x < \frac{\pi}{2},\ sin(x)=sin(\pi -x),\ sin(\pi +x)=sin(2\pi -x)