Trigonometric equations and proving identities
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 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
- One equation, many answers
- Finding all the solutions
Read the transcript of the teaching part
Last time
Before we start: last time, in Trigonometric graphs and the Pythagorean identities, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
One equation, many answers
Ask for the angle whose sine is a half, and your calculator says thirty degrees. But a hundred and fifty degrees works too, and so does thirty plus three sixty. A trig equation has a whole family of answers, and the range in the question tells you which ones to keep.
Finding all the solutions
Find the first value with inverse sine, cosine or tangent. This is the principal value. Sine is positive in two quadrants. So the second solution is one eighty minus the first. Cosine: the second solution is three sixty minus the first. Tangent: add one eighty. Then add or subtract full turns to find every solution inside the range.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Proving trigonometric identities · Solving trigonometric equations.
The whole chapter: Simultaneous Equations, 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.