Can anyone help to check if my communication skill for part B is good enough please?

The question is as following:

Part a:

transform into the form r \sin (\theta + \alpha), where r > 0 and .

>>>>> my ans obtained is

[tex]\sqrt{13} \sin (\theta + 33.7 deg)[/tex]

Part B

Given that , find the value of k such that the equation

has a unique solution.

>>>>>>>>>>my answer:

first I sketched (not draw) a graph of [tex]\sqrt{13} \sin (\theta + 33.7 deg)[/tex]

then :

Given

ie

From the sketched graph, it is only possible for k to have a unique solution, where when [tex]\sqrt{13} [/tex]