sin(x) = cos (x)

[Chavi]

What is the best way to solve equations such as sin(x) = cos(x) or sin(x) = -cos(x) and the like. .
Thanks

[fady_22]

Change it into tan(x) i.e sin(x)=cos(x) is the same as tan(x)=1.

[TrueTears]

sin(x)-cos(x) = 0

multiply by sqrt{2}/2 on each side.

and then use the compound angle formula!!!

[Martoman]

sin(x)-cos(x) = 0

multiply by sqrt{2}/2 on each side.

and then use the compound angle formula!!!

Um no. Just no. I don't think many people will have it memorized. fady_22 said it right.

Also, be wary of dividing when you have multiple factors of trigonometric functions, ie: don't just divide by cos(x) because this deletes some solutions rather:




Null factor:

or implies

Solve these two questions and quote your solutions over the required domain. If you just divided, you would only be solving case 2 of the above two cases. Just be careful of this that's all.

[TrueTears]

?

saying no to an ingenious technique taught me to by Ahmad? that's saying no to a maths god

[Mao]

?

saying no to an ingenious technique taught me to by Ahmad? that's saying no to a maths god

Martoman doesn't want to do that because:

A. It will get people extremely confused
B. There is a much simpler alternative
C. He doesn't want to commit intellectual faggotry
D. All of the above

[TrueTears]

but people dont know when to divide trig identities coz it gets rid of solutions, its elegant solution, not confusing at all, it is just as valid as the alternate solution so i dont see whats wrong about it, why wud u want to reject such an aesthetically pleasing solution, thats plain rude towards mathematics

[Mao]

but people dont know when to divide trig identities coz it gets rid of solutions, its elegant solution, not confusing at all, it is just as valid as the alternate solution so i dont see whats wrong about it, why wud u want to reject such an aesthetically pleasing solution, thats plain rude towards mathematics

Um no. Just no.

[TrueTears]

Um yes. Just yes.

[enwiabe]

Dividing by cosx in this case does not get rid of any solutions as no information has been deleted.

You only get deletion of information when you cancel terms in a null factor setting (or take only the positive or negative in a square root).

I think, TT, given that the knowledge gap shown indicates a fair amount of struggle with the concepts, that detailing a nuanced and very much advanced technique (as shown by the fact that ahmad had to teach it to you) is not only not helpful, but in fact counter-productive to the student's learning.

It is a good technique, but it is not a good technique when you're trying to learn the basics. I think you need to exercise a bit more tact here

[/0]

I don't see what all the fuss is about this technique. You wouldn't have told Ahmad to shush would you? This is the specialist maths forum, people should be familiar with the sine and cosine expansions. I think it is an elegant alternative technique which, given the material covered in specialist maths, shouldn't cause much confusion once it is shown to you.
I remember that when I had similar questions about sin(x) = cos(x) and I read Ahmad's post I was intrigued by it, and I've remembered the method ever since. It's always a pleasure to witness a touch of genius every now and then.

If it was something outside of the specialist course then maybe it would cause undue confusion. But this is clearly in the syllabus.

[TyErd]

Can someone link me to Ahmads post please?

[Martoman]

?

saying no to an ingenious technique taught me to by Ahmad? that's saying no to a maths god

Martoman doesn't want to do that because:

A. It will get people extremely confused
B. There is a much simpler alternative
C. He doesn't want to commit intellectual faggotry
D. All of the above

she. i know, my name seems to suggest the contrary. Its a nickname.

*edit* my comment was embedded in a quote from another person >.<

[the.watchman]

?

saying no to an ingenious technique taught me to by Ahmad? that's saying no to a maths god

Martoman doesn't want to do that because:

A. It will get people extremely confused
B. There is a much simpler alternative
C. He doesn't want to commit intellectual faggotry
D. All of the above

she. i know, my name seems to suggest the contrary. Its a nickname.

Lol, more people falling into the evil trap...

[TyErd]

whats your real age martoman