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DIFFERENCE BETWEEN A SINE WAVE AND A COSINE WAVE
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⚡ Alternatively, we can also say that a sine wave is a cosine wave that has been shifted in the other direction by --90°.

📌 Either way, when dealing with sine waves or cosine waves with an angle, the following rules will always apply.

⚡ SINE AND COSINE WAVE RELATIONSHIPS

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cos(ωt+θ)=sin(ωt+Φ+90∘)

sin(ωt+θ)=cos(ωt+Φ−90∘)
📈 When comparing two sinusoidal waveforms, it is more common to express their relationship as either a sine or a cosine with positive-going amplitudes. This is achieved using the following mathematical identities.

⚡ SINE AND COSINE IDENTITIES
sin(A±B)=sinAcosB±cosAsinB
cos(A±B)=cosAcosB∓sinAsinB

⚡ THEREFORE

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−sin(ωt)=sin(ωt±180∘)
−cos(ωt)=cos(ωt±180∘)
±sin(ωt)=cos(ωt∓90∘)
±cos(ωt)=sin(ωt±90∘)
📌 By using these relationships above, we can convert any sinusoidal waveform with or without an angular or phase difference from either a sine wave into a cosine wave or vice versa.

⚡ WHY THIS IS IMPORTANT

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🔹 Helps simplify AC circuit calculations.
🔹 Makes waveform comparison easier.
🔹 Useful in phase angle analysis.
🔹 Important in signal processing and electronics.

⚡ NEXT LESSON – PHASORS

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📘 In the next tutorial about Phasors, we will use a graphical method of representing or comparing the phase difference between two sinusoids.

⚡ We can do this by looking at the phasor representation of a single-phase AC quantity along with some phasor algebra relating to the mathematical addition of two or more phasors.

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✍️ Written by Sisira Senevirathna