How Do You Determine the Phase Constant for Combined Light Waves?

[roam]

Homework Statement

We have two waves with functions:

$$E_1 = 6 \ sin (100 \pi t)$$

$$E_2 = 8 \ sin (100 \pi t + \frac{\pi}{2})$$

Find $$E_1 + E_2$$.

Homework Equations

$$\phi = \frac{2 \pi}{\lambda} \delta = \frac{2 \pi}{\lambda} d sin \theta$$

$$\frac{\delta}{\lambda}=\frac{\phi}{2 \pi}$$

The Attempt at a Solution

The answer to this problem should be $$10 \ sin (100 \pi t + 0.927)$$
I can't understand how they got the value for the phase constant phi to be 0.927. I can't understand how they got the value using the above equations... because we don't know and can't find many variables in those equations. And I'm not sure how to use trig fro this... Any help with this problem is greatly appreciated.

 

[Pi-Bond]

Let

$E_1 + E_2 = Asin(100 \pi t + B)$

Use this and compare coefficients to get the values of A and B. You might want to use the sine addition formula on $E_2$ to first simplify that expression.

 

[mstud]

Maybe you will want to try to find the method yourselves by reading this section on linear combinations:

http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Linear_combinations"

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