Graph of Cosine
The cosine curve is sine shifted left by π/2.
About this topic
The cosine graph has the same wave shape as sine but starts at its maximum of 1 when x = 0, crosses zero at π/2, reaches −1 at π, and completes a cycle at 2π. It is sine shifted left by π/2: cos x = sin(x + π/2).
Cosine is an even function, symmetric about the y-axis. Its period is 2π, amplitude 1, domain all real numbers and range [−1, 1]. Since it is the x-coordinate of a point moving around the unit circle, it measures the horizontal position of that point.
Example: a mass on a spring pulled 5 cm and released at time zero has position 5 cos(ωt), because it starts at maximum displacement. A Ferris wheel rider starting at the top follows a cosine curve, whereas one starting at the middle follows a sine curve. Choosing between sine and cosine for a model is often just about where the clock starts.
Tips: remember that cos 0 = 1, the graph is the mirror image across the y-axis, and cosine and sine are the same curve up to a horizontal shift, so either can model any wave. Check the key points at multiples of a quarter period when sketching.
Key ideas
- Starts at its maximum
- Even function
- Same amplitude and period as sine
Quick check
Use cases: where Graph of Cosine helps
- Homework: review the key idea behind Graph of Cosine before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Graph of Cosine without notes.
- Visual learning: play with the interactive lab to see how Graph of Cosine changes when you adjust its inputs.
- Teaching a friend: explain Graph of Cosine 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 Cosine?
The cosine curve is sine shifted left by π/2.
What will I learn in Graph of Cosine?
Starts at its maximum. Even function. Same amplitude and period as sine.
Is Graph of Cosine 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 Cosine 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 Cosine?
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.