# periodic functions help!!

• Dec 3rd 2010, 07:55 AM
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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
• Dec 3rd 2010, 11:18 AM
emakarov
You can see the formula on this Wikipedia page (starting with "More generally..."). In those notations, a = 7, b = 5 and $\displaystyle \alpha=\pi/4$. The number $\displaystyle 0.707=\sin\alpha=\cos\alpha$. In my calculations, $\displaystyle c\approx11.113$ and $\displaystyle \beta\approx0.324$, so the answer is $\displaystyle c\sin(vt+\beta)$ (this needs double-checking).