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