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

The question is as following:

Part a:

transform $\displaystyle 2 \cos(\theta) + \sin(\theta) $ into the form r \sin (\theta + \alpha), where r > 0 and $\displaystyle 0 \deg < \alpha < 90 \deg $.

>>>>> my ans obtained is

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

Part B

Given that $\displaystyle - \alpha \<= \theta \ <= 180\deg - \alpha$, find the value of k such that the equation

$\displaystyle 2\cos \theta + 3 \sin \theta = k$

has a unique solution.

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

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

then :

Given $\displaystyle - \alpha \<= \theta \ <= 180\deg - \alpha$

ie $\displaystyle - 33.7 \deg <= \theta \ <= 146.3 \deg$

From the sketched graph, it is only possible for k to have a unique solution, where $\displaystyle - \alpha \<= \theta \ <= 180\deg - \alpha$ when [tex]\sqrt{13} [/Math]