Calculating supply voltage in sinusoidal form.

Question

I have the question "The voltages across three components in a series circuit when connected across an a.c. supply are:

$V_{1} = 30\sin(300\pi t - \frac{\pi}{6})$

$V_{2} = 40\sin(300\pi t + \frac{\pi}{4})$

$V_{3} = 50\sin(300\pi t + \frac{\pi}{3})$

Calculate the supply voltage in sinusoidal form."

Here is my attempt:

The final answer I get is $94.97\sin(300\pi t + 0.609) V$.

However when I checked the solutions the answer should be:

$97.39\sin(300\pi t + 0.620) V$

So where have I gone wrong ?

Answer 1

Note that: $$\frac{\pi}{6} \text{ rad} \neq 35^{\circ}$$ However, it is true that: $$\frac{\pi}{6} \text{ rad} = 30^{\circ}$$ Try solving it again, and you should get the correct answer.