Free taster
5 of 6 sections open
The Language of Waves
The Language of Waves
Every sound wave, every radio signal, every heartbeat on an ECG monitor follows a mathematical wave pattern. The sine and cosine graphs are the mathematical description of these waves — smooth, repeating curves that oscillate between a maximum and minimum value. Understanding their shape, key points, and transformations allows you to model anything that repeats periodically: tides, seasons, alternating current, and circular motion.
Describe the key features of the sine graph y = sin x: Shape: smooth wave (S-shaped repeating curve)
Amplitude: 1 (max value = 1, min value = -1)
Period: 360° (repeats every 360°)
Passes through: (0, 0), (90°, 1), (180°, 0), (270°, -1), (360°, 0)
Symmetry: origin symmetry (odd function)
Mathematics glossary
- Describe the key features of the sine graph y = sin x
- Shape: smooth wave (S-shaped repeating curve) Amplitude: 1 (max value = 1, min value = -1) Period: 360° (repeats every 360°) Passes through: (0, 0), (90°, 1), (180°, 0), (270°, -1), (360°, 0) Symmetry: origin symmetry (odd function)
Earn the mark scheme marks
💡 Exam Tips for Trigonometric Graphs
- Learn the 5 key points for each wave (0°, 90°, 180°, 270°, 360°) — you can sketch from these alone
- Period vs amplitude: period is the horizontal width of one cycle; amplitude is the vertical height from the midline
- Multiple solutions: if asked to solve sin x = k or cos x = k in a range, always check for a second solution using symmetry
- tan at 90°: always show the asymptote — the tan graph does NOT cross x = 90°
- Transformation direction: sin(x + 30°) moves LEFT by 30° (inside bracket = opposite direction)
Now try it yourself
Quiz · Question 1 of 11
What is the period of the graph y = sin x?
Tap an answer to check it