Trigonometric Graphs
The sine and cosine graphs are repeating waves with period 360 degrees, while the tangent graph repeats every 180 degrees.
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Play with the controls to see the idea in action.
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The sine and cosine graphs are repeating waves with period 360 degrees, while the tangent graph repeats every 180 degrees.
- Sine starts at 0 and cosine starts at 1
- Amplitude is the maximum height
- Tangent has vertical asymptotes
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Trigonometric Graphs?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Trigonometric Graphs. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Trigonometric Graphs in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Trigonometric Graphs gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Trigonometric Graphs in detail
The graphs of y = sin x and y = cos x are smooth waves that repeat every 360°, oscillating between −1 and 1. The cosine graph is the sine graph shifted 90° to the left. The tangent graph repeats every 180°, passes through the origin and has vertical asymptotes at 90°, 270° and so on.
Changing the equation changes the wave: y = a sin x changes the amplitude, y = sin bx changes the period and adding a constant shifts it up or down. These graphs model periodic phenomena such as sound waves, tides, alternating current and seasonal temperatures, and they help solve trigonometric equations.
How the interactive helps you understand Trigonometric Graphs
Change the angle or let it animate. The horizontal and vertical lengths on the circle show the cosine and sine values for that angle.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Trigonometric Graphs.
Real-life uses and examples
- Explain Trigonometric Graphs to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Trigonometric Graphs in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Trigonometric Graphs by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Trigonometric Graphs without checking why they work.
- Forgetting units, signs or brackets when you apply Trigonometric Graphs.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Trigonometric Graphs
What is Trigonometric Graphs?
The sine and cosine graphs are repeating waves with period 360 degrees, while the tangent graph repeats every 180 degrees.
What are the most important points about Trigonometric Graphs?
The main points are: Sine starts at 0 and cosine starts at 1; Amplitude is the maximum height; Tangent has vertical asymptotes.
Why is Trigonometric Graphs useful?
Understanding Trigonometric Graphs gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Trigonometric Graphs?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Trigonometric Graphs?
Related topics in Mathematics include Volume of Prisms, Units and Conversions, Vectors.