Trigonometry · Grades 10 to 12
Sine and cosine graphs
Find the period of a wave.
The idea
The sine and cosine functions repeat forever. One full repeat is called the period.
For y = sin(bx) or y = cos(bx), the period is 2π divided by b. A larger b makes the wave repeat faster.
Worked examples
- How to Find the Period of a Sine Function Find the period of y = sin(3x). Three steps with the 2pi over b rule, the reason for it, and the b-value mistakes to avoid.
- How to Find the Period of a Cosine Function Find the period of y = cos(4x). Three steps with the 2 pi over b formula, the reason for it, and the b-value mistakes to avoid.
- How to Find the Amplitude of a Sine Wave Find the amplitude and period of y = 5 sin(2x). Three steps that read A and b from the function, with the A-versus-b mistakes to avoid.
Practice this topic
3 problems with answers.