Reduce 5x - 12y + 39 = 0 to the normal form x cosα + y sinα = p…

Step 1. Make the right side positive. $5x - 12y = -39$ becomes $-5x + 12y = 39$.

Step 2. Divide by $13$. $-\dfrac{5}{13}x + \dfrac{12}{13}y = 3$.

Step 3. Read the parts. $\cos\alpha = -\dfrac{5}{13}$, $\sin\alpha = \dfrac{12}{13}$ and $p = 3$.

Step 4. The angle. The cosine is negative and the sine positive, so $\alpha$ is in the second quadrant: $\alpha = 180^\circ - 67.38^\circ = 112.62^\circ$.