Graph of Sine
The sine curve oscillates between −1 and 1 with period 2π.
About this topic
The sine graph is a smooth wave that starts at 0, rises to 1 at π/2, returns to 0 at π, falls to −1 at 3π/2 and finishes a cycle at 2π, then repeats. Its period is 2π, amplitude 1, domain all reals and range [−1, 1].
It is an odd function, symmetric about the origin. Sine waves are produced by tracking the height of a point moving around the unit circle at constant speed, so the graph is a record of circular motion unrolled over time. Key points to plot are the zeros, maximum and minimum, spaced a quarter period apart.
Sine waves model sound tones, ocean tides, alternating current, seasonal temperatures and a swinging pendulum. Combining several sine waves with different frequencies can build any complicated sound, which is the idea behind music synthesisers and audio compression.
Tips: sketch one cycle with five key points, remember that sin 0 = 0 whereas cos 0 = 1, and do not confuse the x-axis units; if the angle is in radians, label the axis with multiples of π/2. Students often draw sine as pointy; it should be smooth and rounded at the peaks.
Key ideas
- Starts at 0 and rises
- Amplitude is the max height
- Period is the cycle length
Quick check
Use cases: where Graph of Sine helps
- Homework: review the key idea behind Graph of Sine before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Graph of Sine without notes.
- Visual learning: play with the interactive lab to see how Graph of Sine changes when you adjust its inputs.
- Teaching a friend: explain Graph of Sine in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Graph of Sine?
The sine curve oscillates between −1 and 1 with period 2π.
What will I learn in Graph of Sine?
Starts at 0 and rises. Amplitude is the max height. Period is the cycle length.
Is Graph of Sine part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Graph of Sine lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Graph of Sine?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.