Question

Determine cos 330° using the cosine sum identity. Be sure to include all necessary work

Answer 1

`\sf (√(3))/(2)`

Explanation:

Cosine sum identity:

`\boxed{\bf Cos \ (A - B) = Cos \ A * Cos \ B + Sin \ A * Sin \ B}`

Cos 360 = Cos 2π = 1 (We know that Cos 2nπ = 1)

`\sf Cos \ 30^\circ = (√(3))/(2)\\\\\\Sin \ 360^\circ = Sin \ 2\pi = 0 \ ~~ [\text{\bf We know that Sin 2n$\pi =0$}]\\\\Sin \ 30^\circ = (1)/(2)`

Cos 330 = Cos ( 360 - 30)

A = 360 and B = 30

= Cos 360 * Cos 30 + Sin 360 * Sin 30

`\sf = 1*(√(3))/(2)+0*(1)/(2)\\\\\\=(√(3))/(2)`