Trig: General Solutions

[asian_91]

Hi, need help with gen solutions!!!

From 0-2 pie

sin^2x = 1/4

2cos^2 theta + cos theta = 0

2 sin^2x = 3 cosx

sin(theta + pie/4) = 1/2

4 sin theta = 5 cos theta ( write in the form of tan)

cos 2 theta + cos theta = 0

sin 2 theta + cos theta = 0

2 tan theta + cot theta = 3

Thanks!

[stonecold]

For general solutions to trig equations just use the following formulae:





where n=Z

[stonecold]

And those aren't general solutions which you've posted up.  They all have actual solutions.

General solutions are for where you aren't given a domain...

Just use algebra and the exact values for sin, cos and tan where theta = 30, 45, 60 and 90 degrees.

[vea]

Hey stonecold what textbook are you using?
I'm just curious because my textbook gives a different general solution for sine equations which works but seems longer compared to the one you've posted.

Cheers

[Yitzi_K]

Vea I think there's two different expressions for the general solution for sin.

Side question, do we have to know this stuff? My teacher never even mentioned it, nor did my spesh teacher.

[fady_22]

Vea I think there's two different expressions for the general solution for sin.

Side question, do we have to know this stuff? My teacher never even mentioned it, nor did my spesh teacher.

Yeah, it comes up in exams.

[vea]

Vea I think there's two different expressions for the general solution for sin.

Side question, do we have to know this stuff? My teacher never even mentioned it, nor did my spesh teacher.

Yeah the one I learnt is



The first one is for the solution in the first quadrant while the second one is for the solution in the second quadrant.

[the.watchman]

Actually, I really like stonecold's , it's rather smart

Logically though, you can just work out simple solutions first, then add or on the end to suit.
This is easier to apply in an exam situation

[vea]

Actually, I really like stonecold's , it's rather smart

Logically though, you can just work out simple solutions first, then add or on the end to suit.
This is easier to apply in an exam situation

stonecold's method seems much shorter and less prone to mistakes. Can't be bothered learning it anymore since I've already got my other formula... haha lazy

[Blakhitman]

Vea I think there's two different expressions for the general solution for sin.

Side question, do we have to know this stuff? My teacher never even mentioned it, nor did my spesh teacher.

Yeah the one I learnt is



The first one is for the solution in the first quadrant while the second one is for the solution in the second quadrant.

Yea stonecold's is like a joined one with both.

[nbalakers24]

after you found the general solution how do find all the solutions for x in the interval of (-pie,pie) or (-1,1)?

thanks

[the.watchman]

Sub in different (integer) values of n to get your answers

[nbalakers24]

ohhh thought so but book had diff i think they used -1, -2, -3 :S

thanks mate

[schnappy]

I hate using letters in maths... I think like this for a general soln:
x = your angle +- period*n, n belongs integers (Z)
x = your other angle +- period*n, n belongs integers (Z)

It's much the same as above, just expressed in a way I like. I found general soln much easier to understand if you look at them graphically on the circle... you have an angle, say pi/4, add a period (2pi) and youll be there again - you can do this infinite times. Same for your other angle... I leave it as I've written it above, dont put it all into one equation with a +- in it or whatever... just leaves more room for error. It's not like it's a vital skill you'll need in your life anyway! And if you do, you'll have a calculator

[kenhung123]

What's confusing me with this stuff is why is the equations so complicated and stuff when you can just add 2pi to each solution for 1 cycle? Such as x=pi/3+2pi*k where k is an integer