transforming graph of sin x

Hi guys.
there's equation that I'm trying to sketch the graph of it which looks so complicated but the text book has made it much more easier by turn it into another equation which didn't explain it how, i just attached the question here i understand how the graph of sin x will be transformed to give you this but the text book has turned the first equation to the easier one confusing me. would appreciate a clear explanation. thanks

Have you not covered the harmonic form?

They've said that $5sinx-5 \sqrt{3}cosx \equiv R sin(x+\alpha)$ and worked out $R$ and $\alpha$.