Need help with solving trig equations

[lolaishappy]

Hey guys, this is yr11 question that I've  struggled awhile with, which is solving trig equations. Without using a calculator, so yeah.
Question:
Find the equation of x
2cos x - (square root)2 = 0 
domain: [-180,360]

Since this is methods, can someone suggest a method to solve this. I'm desperate man Dx

p.s I remember my teacher, doing a method like let cosx equal to a, then times it by the domain or something?

[IndefatigableLover]

Your domain is [-180, 360] or

(Transpose everything by adding and dividing to get) -



Okay so we know from this, our basic angle is and because it's positive, we will be taking values from where cosine is positive along the unit circle (to which you know is Quadrants 1 and Quadrants 4).

So we'll start at and move from Quadrants 3 -> Quadrants 4 and we find that Quadrant 4 is something we want. To get that, we just go: which is
As we move from Quadrants 4 -> Quadrants 1, this is another desired result and we can find it by doing: which is

Now we move along the unit circle till we go back to Quadrant 4. This will be the same result as our previous answer but we add to it to get

Therefore our final answer is:



If you need anything to clarify with then just reply back!

EDIT: With that last part where you said your teacher times something to the domain, that is correct in getting the right amount of solutions.

Say you had and you were told to solve from [0,360], you would multiply the domain by a factor of 2 making your domain [0, 720] which is where you'll be taking your solutions from. Just remember that now that you've done this, your answer won't be 'x=..' but '2x=...' so you must further divide everything by two to get it down to 'x' (which also makes everything fit in the original domain).

[lolaishappy]

Nice reply, I totally just read it like a prep, but I get it lol. Just one thing you said  "this is another desired result and we can find it by doing:  which is 0 + pi/4.... Umm where did you get 0, what do you mean 0??

[keltingmeith]

Nice reply, I totally just read it like a prep, but I get it lol. Just one thing you said  "this is another desired result and we can find it by doing:  which is 0 + pi/4.... Umm where did you get 0, what do you mean 0??

Because you start from 0 and move up pi/4 - this puts you in the first quadrant.

[lolaishappy]

Because you start from 0 and move up pi/4 - this puts you in the first quadrant.

Ah of course, thanks bro and other bro