Period and Frequency
Length of one cycle and cycles per unit.
Key idea
Length of one cycle and cycles per unit.
In depth
For y = sin(Bx), the period is 2π/|B|, the length of one full cycle. Frequency is 1/period, the number of cycles per unit. Larger B squeezes the wave.
Worked example
y = sin(3x) has period 2π/3, and completes 3 cycles in 2π.
Formula
Real-world uses
- Setting the pitch of a musical note
- The frequency of mains electricity (50 Hz or 60 Hz)
Common mistake
Using B as the period rather than 2π/B.
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 Period and Frequency?
Length of one cycle and cycles per unit. It is a topic at the intermediate level in Trigonometry.
What is the formula for Period and Frequency?
The key formula is T = 2π/B, f = 1/T.
Where is Period and Frequency used in real life?
Real-world examples: Setting the pitch of a musical note; The frequency of mains electricity (50 Hz or 60 Hz).
What should I learn before Period and Frequency?
Make sure you are comfortable with Amplitude, the previous topic in Trigonometry.
What is a common mistake with Period and Frequency?
Using B as the period rather than 2π/B.
How can I practise Period and Frequency?
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 Period and Frequency?
Move on to Phase Shift next.
Related intermediate topics in Trigonometry
- Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
- Converting Degrees and Radians – Multiply by π/180 or 180/π.
- Sine Ratio – Opposite over hypotenuse.
- Cosine Ratio – Adjacent over hypotenuse.
- Tangent Ratio – Opposite over adjacent.
- Reciprocal Trig Functions – Cosecant, secant and cotangent.