periodic functions help!!

hi guys new here, looking for help and advice and here to help others.

Currently studying maths in engineering

Looking at a question as follows:

Two are: 7sin vt and 5sin(vt + p/4)

Use phasors and calculation to combine the two functions, expressing the result in Rsin (vt + alpha)

This is what I have got

y=7sin vt
y=5sin (vt + p/4)
y=7sin vt + 5sin (vt + p/4)
y=Rsin (vt+a)

co sine rule:

a squared = b squared + c Squared – 2b.cosA

a squared = 5 squared + 7 squared – 2 x 5 x 7 – 0.707

a squared = 74

Am I on the right lines, I am using an example did previus but cant work out where the 0.707 comes from

Help in doing this be great

You can see the formula on this Wikipedia page (starting with "More generally..."). In those notations, a = 7, b = 5 and . The number . In my calculations, and , so the answer is (this needs double-checking).