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: 5 worked examples, 4 practice questions, 1 real past-paper question with the answer 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 Circles and chords, sectors in r and theta, and tangents with sectors, 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.
Chapter 1.5: Trigonometry
- Trigonometric graphs and the Pythagorean identities 5 min
- Trigonometric equations and proving identities 6 min
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.