Solve the following equation for $0^\circ < x < 360^\circ$
$$\cos(2x - 15^\circ) = -0.145$$
By finding out the cos inverse, I get $81.7^\circ$. Because $-0.145$ is negative, it lies on the 2nd and 3rd quadrant. That is we can find $x$ by $(180 + \theta)$ and $(180 - \theta)$.
So this was what I've thought:
$$2x-15^\circ = 81.7^\circ$$
From here according to me, $$x=(81.7^\circ + 15^\circ)/2$$ gives $$x=48.4$$ which is not the answer in my book.
Then comes $$2x-15^\circ=(180+81.7^\circ),(180-81.7^\circ)$$
From here I find $$x=138.35^\circ, 56.7^\circ$$ these answers are correct.
Now, the first answer $48.4$ is wrong, and there is one more answer in my book, i.e, there are $4$ values in the answer, where I got $3$ answers and $1$ is wrong.
Could someone help help me to find the two other answers?