rewrite sin(x+π/6) in terms of sinx and cosx .

Question

this is pre calculus I can't seem to find this in our notes anywhere so i'm not sure this was even taught to us

Answer 1

Hi Steaac.

This problem involves the use of Sine of the Sum of Angles Identity AND knowledge of the Unit Circle.

I know Identities and a pain in the behind, because they require a lot of memorizations, but they're an important part of trig. If your teacher skipped Identities (Maybe because of the pandemic) you should be able to find lists of them on the internet.

The Sine of the Sum of Angles Identity reads as; Sin (A+B) = Sin(A)Cos(B) + Cos(A)Sin(B).

In this problem, A is x and B is π/6.

Just substitute these into the identity and we get; Sin(x)Cos(π/6) + Cos(x)Sin(π/6).

BUT WAIT!

π/6 is a special angle. Sin(π/6) = 1/2 and Cos(π/6) =√3/2.

Substituting these we get; 1/2Sin(x) + √3/2Cos(x)

I hope this helps.