1. sin(x) + sqrt2 = - sinx
2. 3 tan(x/2)+3=0
3. solve for cosx ; cos x =1/2
Hello william
1
Add to both sides, and subtract from both sides:
Now I'm not sure what sort of answer is needed now. Do you use a calculator to work out a single answer for , giving your answer in degrees? Or do you want lots of answers in radians, involving things like and ?
I don't know. But in degrees, possible answers include , , and so on.
2
Again, you have lots of possibilities now. One answer is that
So
There are lots of other possibilities...
3
By now, I'm guessing that you want all the possible values of if
I reckon the easiest way is to look at a sketch graph of , and work them out from that.
The first positive value is (or radians), but there's another on the other side of the y-axis, where ( )
The graph repeats every , or radians, so you get more answers by adding ( radians) on to these two answers. So in degrees:
I'll leave it to you to find these answers in radians, if you need to.
Grandad