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4. The electric field of an electromagnetic wave $\vec{E} = \hat{a}_x E_0 \cos \left[ 2 \times 10^8 \pi \left( t - \frac{z}{c} \right) + \theta \right]$ is the sum of $\vec{E}_1 = \hat{a}_x 6 \sin \left[ 10^8 \pi \left( t - \frac{z}{c} \right) + \frac{\pi}{6} \right] \cos \left[ 10^8 \pi \left( t - \frac{z}{c} \right) + \frac{\pi}{6} \right]$ and $\vec{E}_2 = \hat{a}_x 4 \cos \left[ 2 \times 10^8 \pi \left( t - \frac{z}{c} \right) - \frac{\pi}{3} \right].$ Find $E_0$ and $\theta$.

          4. The electric field of an electromagnetic wave
\(\vec{E} = \hat{a}_x E_0 \cos \left[ 2 \times 10^8 \pi \left( t - \frac{z}{c} \right) + \theta \right]\)
is the sum of
\(\vec{E}_1 = \hat{a}_x 6 \sin \left[ 10^8 \pi \left( t - \frac{z}{c} \right) + \frac{\pi}{6} \right] \cos \left[ 10^8 \pi \left( t - \frac{z}{c} \right) + \frac{\pi}{6} \right]\)
and
\(\vec{E}_2 = \hat{a}_x 4 \cos \left[ 2 \times 10^8 \pi \left( t - \frac{z}{c} \right) - \frac{\pi}{3} \right].\)
Find $E_0$ and $\theta$.

4. The electric field of an electromagnetic wave
E⃗ = âx E0 cos[ 2 × 10^8 π( t - (z)/(c)) + θ]
is the sum of
E⃗1 = âx 6 sin[ 10^8 π( t - (z)/(c)) + (π)/(6)] cos[ 10^8 π( t - (z)/(c)) + (π)/(6)]
and
E⃗2 = âx 4 cos[ 2 × 10^8 π( t - (z)/(c)) - (π)/(3)].
Find E0 and θ.

Added by Eva H.

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