Maths (Harmonic equations)

How do i find k, in this question?

sinθ+√2cosθ=k

Answer is -√3≤k≤√3, but how do i arrive at that?
Its core 3 AlevelMaths under the trigonometry topic.

Let f(x) = sinθ+√2cosθ

Put it in the form of Rcos(θ + a)

Work out the range of that function and that'll give you k

You can't really solve for theta because you don't know what k is, so you just try simplify it and see where that takes you.

Also I've done that question before

I think it was a C3 paper

How does one find the value of the constant k for.... sin θ+Root(2)Cos θ=k

I'm Year 13, I was supposed to get an A* but my brain melted in the C3 exam due to how hot it was and me leaving my water bottle in the fridge. I expect an A but I may get an A*. I'll probably average 90% in total though, which sucks

you can find R and α to get RCos(θ - α)

but they would have to tell you a value for k.

Revise from the get go. A paper a week for Maths and don't hesitate to do IAL C34 papers.

Go over your weaknesses once you identify them. There's no point in doing papers unless you improve areas in which you consistently fail in.

Try and revise backwards too once you finish A2 so your AS content is fresh in your mind