Auxiliary Angle/Examples
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Examples of Auxiliary Angles
$3 \cos x$ minus $2 \sin x$
- $3 \cos x - 2 \sin x = \sqrt {13} \map \cos {x + \arctan \dfrac 2 3}$
Hence the greatest value of $3 \cos x - 2 \sin x$ is $\sqrt {13}$ which happens when $x = -\arctan \dfrac 2 3$.
Solutions to $3 \cos x - 2 \sin x = 1$
Consider the equation:
- $(1): \quad 3 \cos x - 2 \sin x = 1$
The solutions to $(1)$ between $0 \degrees$ and $360 \degrees$ are:
\(\ds x\) | \(=\) | \(\ds 40 \degrees \, 20'\) | ||||||||||||
\(\ds x\) | \(=\) | \(\ds 252 \degrees \, 24'\) |