Hi folks,

I am trying to find the general solution to a trig equation:

I get to $5 sin (\theta + 53.1\circ) = 1$

so $(\theta + 53.1) = sin^{-1}(\frac{1}{5}) = 11.5\circ $

so I think the general solution is $\theta + 53.1 = 180\circ n + (-1)^n 11.5\circ$

i.e. $\theta = 180\circ n + (-1)^n -41.6\circ$

the answer in my maths books is $360\circ n + 115.3\circ , 360\circ n - 41.6\circ$

I can understand the second solution but not the first.

I could have simplified the second equation to $\theta = -41.6$ with solutions at 41.6 and 221.6

Or I could have $\theta + 53.1 = 11.54$ and $(180 - 11.5)$

I am not sure which order to do things.