Domain question (Trig)

[TommyLie]

Textbook Q: Find x such that:     Textbook Sols:

So:





Domain becomes:

(< means greater than or equal to)



Therefore:



The thing I didn't understand in the solutions book was how they altered the domain:

Domain became: (< means greater than or equal to)

I understand that they have must have multiplied it by 2 and subtracted 30 from it (Well I assume this is what they have done), but why do it in this order? if you sub 30 and times by 2 you get a different domain, so my question is how do you know which way to do it?

Cheers

[tony3272]

You consider the transformations on the variable x that you have.
You start with x and you end up with 2x-30.
The way to do that is to multiply by 2 first and then subtract 30. Doing it the other way will result in 2(x-30). So that's the order which you must alter your domain.

[TommyLie]

Thankyou! Also, how would you use the half angle formula to find exact values of ?

[tony3272]

Hey no problem!
For the second problem it's essentially the same as using the double-angle formula. So:





Then just solve for from there.

[TommyLie]

I don't understand...How did you get ?

The Half Angle Formular i'm using is

Which gives:



Where u is the angle. And the angle is

So that means i get:
                                                   =?