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[h] SL 3.2 Use of sine, cosine and tangent ratios
[q] Number of solutions
[a] If you look at a \(sin\) curve, you may notice that it passes the vertical line test, but fails the horizontal line test. What this tells us that when you do \(sin\) of an angle you get one answer only. However, when you do \(sin^{-1}\) of a value (to find a missing angle), you get multiple answers in fact- infinte answers/angles.
[q] Restricted Domain
[a] You could, in theory describe your infinite answers. For example \(tanx\) repeats every π. So, you could have \(tanx=1\to x=\frac{π}{4}+kπ, k\in Z\).
It is far more likely that they will give you an interval in which your angle or angles must fall in between.
[q] Hidden Quadratics
[a] We arrange something in the form: \(asin^2x+bsinx+c=0\), change to \(aX^2+bX+c=0\), solve for X, get \(sinx\) equal to the values, then solve.
Clearly the same process applies for a \(cos\) or \(tan\) quadratics.
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