So as a part of my extended essay I am looking into the importance of complex numbers in signal processing. I am in high school, but I cannot seem to figure out how to multiply two sinsoids together without the use of complex numbers. There has to be a way. Here is the two that I am trying to multiply, $$3\cos\left(\omega t + \frac{\pi}{4}\right) \times 0.5 \cos \left(\omega t - \frac{3\pi}{8} \right)$$ Can someone please help me out?
2026-04-07 00:40:34.1775522434
How to multiply two sinusoids with the same frequencies but are out of phase without the use of complex numbers.
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You can use the identity: $$\cos A \cos B = \frac{1}{2}[\cos (A + B) + \cos (A - B)]$$