Trigonometric graphs and the Pythagorean identities
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 4 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- A wave you can write down
- The basic shapes
- Transformations
Read the transcript of the teaching part
Last time
Before we start: last time, in Arc length, sector area and shaded regions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
A wave you can write down
Tides, sound, alternating current. All of them rise and fall in a smooth repeating wave. Four numbers describe any such wave: how high, how fast, how far up, and where it starts. You will read them from the equation.
The basic shapes
The sine curve starts at zero, rises to one at ninety degrees, and repeats every three hundred and sixty degrees. The cosine curve is the same wave, starting at its maximum of one. The tangent curve repeats every one hundred and eighty degrees, with vertical asymptotes at ninety degrees and its odd multiples.
Transformations
In y equals a sine b x plus c: a stretches the wave. The amplitude is a. The number b squeezes the wave sideways. The period is three hundred and sixty degrees over b, or two pi over b. The number c shifts the whole wave up. The midline is y equals c, and the range runs from c minus a to c plus a.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Graphs of trigonometric functions.
The whole chapter: Trigonometry.
Chapter 10: Trigonometry
- Trigonometric graphs and the Pythagorean identities 5 min
- Trigonometric equations and proving identities 6 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.