sin(x) = cos (x)

[Martoman]

oh 9001. That is: Over 9000.

[qshyrn]

martoman you sound like a guy for some reason. i usually can tell a guy from a girl..  
anyway, the method that TT mentioned is actuaally really useful even though its not the best option in this case. like when  you have something like sin (x)+ cos(x)=1

[brightsky]

martoman you sound like a guy for some reason. i usually can tell a guy from a girl..   
anyway, the method that TT mentioned is actuaally really useful even though its not the best option in this case. like when  you have something like sin (x)+ cos(x)=1

[qshyrn]

martoman you sound like a guy for some reason. i usually can tell a guy from a girl..  
anyway, the method that TT mentioned is actuaally really useful even though its not the best option in this case. like when  you have something like sin (x)+ cos(x)=1

ok, let me change it to something like  3/4 sin(x)+  cos(x)=5/8  , given cos-1(4/5)=37 degrees

[Yitzi_K]

sin(x)-cos(x) = 0

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

and then use the compound angle formula!!!

Could you go through and explain this one please?

[qshyrn]

sin(x)-cos(x) = 0

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

and then use the compound angle formula!!!

Could you go through and explain this one please?

convert sqrt2/2 to cos of something, then you use a compound identity  (the sin one)

[m@tty]

martoman you sound like a guy for some reason. i usually can tell a guy from a girl..  
anyway, the method that TT mentioned is actuaally really useful even though its not the best option in this case. like when  you have something like sin (x)+ cos(x)=1

Shouldn't there also be a solution at ??



...

[TrueTears]

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.

exactly... and how is this method of the spesh course wdf?

ur using algebra manipulation and a compound angle formula... dont tell me the standard of spesh has gone down in 1 year

and yes both me and /0 has a huge orgasm at school when we discussed ahmad's ingenuity the next day

[brightsky]

martoman you sound like a guy for some reason. i usually can tell a guy from a girl..  
anyway, the method that TT mentioned is actuaally really useful even though its not the best option in this case. like when  you have something like sin (x)+ cos(x)=1

Shouldn't there also be a solution at ??



...

Yeah, actually I should've finished off like this, instead of converting the into ...

By the null factor law:

     

etc.....

[Martoman]

martoman you sound like a guy for some reason. i usually can tell a guy from a girl..  
anyway, the method that TT mentioned is actuaally really useful even though its not the best option in this case. like when  you have something like sin (x)+ cos(x)=1

This is the obvious consequence of the fact that there are no women on the internets!! Aha! solved.  :smitten:

[Yitzi_K]

sin(x)-cos(x) = 0

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

and then use the compound angle formula!!!

Could you go through and explain this one please?

convert sqrt2/2 to cos of something, then you use a compound identity  (the sin one)

Yeah nah still not getting it sorry

[qshyrn]

sin(x)-cos(x) = 0

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

and then use the compound angle formula!!!

Could you go through and explain this one please?

convert sqrt2/2 to cos of something, then you use a compound identity  (the sin one)

Yeah nah still not getting it sorry

i didnt explain clearly.   sqrt2/2 can be written as cos(pi/4) or sin(pi/4)   so    
sinx -cosx=1
sqrt(2)/2 sin x- sqrt(2)/2 cos x=1
cos(pi/4)sinx-sin(pi/4)cos x=1
sin(x-pi/4)=1

[Yitzi_K]

Thanks, I've got it now. Although you've made a mistake or two in your answer 

It does seem like an incredible technique, fairly limited in it's application though.

[iffets12345]

martoman you sound like a guy for some reason. i usually can tell a guy from a girl..   
anyway, the method that TT mentioned is actuaally really useful even though its not the best option in this case. like when  you have something like sin (x)+ cos(x)=1

Shouldn't there also be a solution at ??



...

Yeah, actually I should've finished off like this, instead of converting the into ...

By the null factor law:

       

etc.....

just wanted to add, if he had kept going with the solutions for Sin (2x)= 0, you would have gotten pi/2 anyway, as

2x= 0, pi, 2pi...
x= o, pi/2, pi.
So just another way