Solving Trig Equations: How to Verify Identities and Find All Solutions?

[Laceylb]

Here are a few problems i don't know where to start, basically because my trig teacher doesn't teach...but anyways if you have any ideas on any of them, please post

tan(x+PI) - tan(x-PI)= 2 tan x

^ verify the identity





cos(x+y)cos(x-y) = cos^2 x - sin^2 y

^ verify identity



sin(arctan2x-arccosx)

^write as an algebraic expression


and



cos(x + PI/4) - cos(x- PI/4) = 1

^find all solutions

 

[HallsofIvy]

And why, exactly, is it easier to annouce that "atrig teacher doesn't teach" than it is to try anything yourself? Every problem you've given is pretty close to trivial. Perhaps it would have been better to say "Please help me trick my teacher into giving me a passing grade without my having toactually learn anything myself"!

 

[Laceylb]

And why, exactly, is it easier to annouce that "atrig teacher doesn't teach" than it is to try anything yourself? Every problem you've given is pretty close to trivial. Perhaps it would have been better to say "Please help me trick my teacher into giving me a passing grade without my having toactually learn anything myself"!

excuse me, i have a 100 in the class right now, he doesn't show us how to do things and i usually do try and figure them out myself, that is why i resorted to the internet to try and find help, instead of insulting and saying that it is trivial, why don't you explain how to start them if they are so very trivial

 

[berkeman]

instead of insulting and saying that it is trivial, why don't you explain how to start them if they are so very trivial

Because the homework forums require that you start the problems, and we help some when you get stuck. That's what you agreed to when you signed on to PF. C'mon, from the 100% so far thing, it sounds like you can get part-way through these. Show us some starts...

 

[berkeman]

Like, how do you usually solve equations like these so far in your class? Do you often substitute tan() = sin()/cos()? Or do you use other methods?

Here's a trig identity page that I posted a link to in a recent thread, in case it helps:

http://aleph0.clarku.edu/~djoyce/java/trig/identities.html

 

[Laceylb]

Like, how do you usually solve equations like these so far in your class? Do you often substitute tan() = sin()/cos()? Or do you use other methods?

Here's a trig identity page that I posted a link to in a recent thread, in case it helps:

http://aleph0.clarku.edu/~djoyce/java/trig/identities.html

i have all the identities written down... i have the arc problem finished now... i can usually figure out a problem once i find out where to start, but we never went over these... we just use identities for everything

 

[Laceylb]

i also have the last one finished now

 

[Laceylb]

the second one i have started on the left side

=(cosxcosy-sinxsiny)(cosxcosy+sinxsiny) ? is that right and if so, would i make it then cos^2 xcos^2y - sinx^2 xsin^2y or would that defeat the purpose

 

[VietDao29]

the second one i have started on the left side

=(cosxcosy-sinxsiny)(cosxcosy+sinxsiny) ? is that right and if so, would i make it then cos^2 xcos^2y - sinx^2 xsin^2y or would that defeat the purpose

Okay, so far so good.
In the RHS, you have cos²x, and sin²y, right? You can try to change sin²x to cos²x, and cos²y to sin²y and see what you get.
Can you go from here? :)

 

[Laceylb]

Okay, so far so good.
In the RHS, you have cos²x, and sin²y, right? You can try to change sin²x to cos²x, and cos²y to sin²y and see what you get.
Can you go from here? :)

i finished it. it was due today.i asked him and someone else put it on the board..you had to replace cos^2 s with sin^x -1 and sin^2y-1 and it continued from there but i don't really remember the rest