Phasors
Represent sinusoids as rotating complex numbers in electrical engineering.
Key idea
Represent sinusoids as rotating complex numbers in electrical engineering.
In depth
A phasor is a rotating vector or complex number representing a sinusoid A cos(ωt + φ) as Ae^(iφ). Adding sinusoids of equal frequency reduces to adding complex numbers. It is the standard tool for AC circuits.
Worked example
3 cos ωt + 4 sin ωt: phasors 3 and −4i add to magnitude 5, so = 5 cos(ωt − 53°).
Real-world uses
- Solving AC circuit problems with rotating vectors in electrical engineering
Common mistake
Combining sinusoids of different frequencies this way.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Phasors?
Represent sinusoids as rotating complex numbers in electrical engineering. It is a topic at the expert level in Trigonometry.
Where is Phasors used in real life?
Real-world examples: Solving AC circuit problems with rotating vectors in electrical engineering.
What should I learn before Phasors?
Make sure you are comfortable with Sinusoidal Regression, the previous topic in Trigonometry.
What is a common mistake with Phasors?
Combining sinusoids of different frequencies this way.
How can I practise Phasors?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Phasors?
Move on to Lissajous Curves next.
Related expert topics in Trigonometry
- Half Angle Formulas – Trig of θ/2.
- Power Reducing Formulas – Reduce squares to first powers of cos 2θ.
- Product-to-Sum Formulas – Convert products into sums.
- Sum-to-Product Formulas – Convert sums into products.
- Triple Angle Formulas – sin3θ and cos3θ in terms of θ.
- Trig and Inverse Trig Compositions – Evaluate expressions like sin(arccos x).