Question

1A-6 a) Express in the form Asin(x + c)
Can anyone give me some pointers on this, i have no idea how to start, are there trig identies and substitution that has to happen?

Answer 1

\[\sin(A+B)=sinAcosB+cosAsinB\] This is an identity, so that means
\[A*\sin(x+c)=A*(\sin x \cos c+\cos x \sin c)\] To solve this we need to find values for A and c.

Answer 2

We need \[A \sin x \cos c+A \cos x \sin c=\sin x+\sqrt{3} \cos x\]
so \[A \cos c=1\] \[A \sin c=\sqrt{3}\]

Answer 3

That gives us two equations and two unknowns.

Answer 4

Personally, I would square both and then add them together. Factoring out A^2 can then help solve them.