Graph of Sine
A smooth wave with amplitude 1 and period 2π.
Key idea
A smooth wave with amplitude 1 and period 2π.
In depth
y = sin x is a smooth wave with period 2π, amplitude 1, passing through the origin and oscillating between −1 and 1. It is the height of a point moving around the unit circle.
Worked example
Key points per period: (0, 0), (π/2, 1), (π, 0), (3π/2, −1), (2π, 0).
Formula
Real-world uses
- Modelling sound waves, light waves and the up-and-down motion of a tide or a piston
Common mistake
Starting the wave at its maximum; that is cosine.
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 Graph of Sine?
A smooth wave with amplitude 1 and period 2π. It is a topic at the intermediate level in Trigonometry.
What is the formula for Graph of Sine?
The key formula is y = sin x.
Where is Graph of Sine used in real life?
Real-world examples: Modelling sound waves, light waves and the up-and-down motion of a tide or a piston.
What should I learn before Graph of Sine?
Make sure you are comfortable with Coterminal Angles, the previous topic in Trigonometry.
What is a common mistake with Graph of Sine?
Starting the wave at its maximum; that is cosine.
How can I practise Graph of Sine?
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 Graph of Sine?
Move on to Graph of Cosine 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.