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Auxiliary Angle Method

Quiz Details

Topics covered

  • Q 1 Trig Equations (Year 12) - Auxiliary Angle Method

    Year: 2017   Question: 4
    References:

  • Q 2 Trig Equations (Year 12) - Auxiliary Angle Method

    Year: 2017   Question: 7
    References:

  • Q 3 Trig Equations (Year 12) - Auxiliary Angle Method

    Year: 2018   Question: 11c
    References:

  • Q 4 Trig Equations (Year 12) - Auxiliary Angle Method

    Year: 2015   Question: 11d
    References:
Question 1
HSC 2017 - Question 4 (External Link) Show Question
Answer

\(  \frac{1}{2}\)

Worked Solution

\begin{aligned}\text{Let } 2\sin x -\cos x &= \sqrt{5}\sin(x-\alpha)\\&=\sqrt{5}\sin x\cos \alpha -\sqrt{5}\cos x \sin \alpha\\&=\sqrt{5}\cos \alpha \sin x - \sqrt{5} \sin\alpha \cos x\end{aligned}

\begin{aligned}\sqrt{5}\cos \alpha &=2, & \sqrt{5}\sin \alpha =1\\\cos \alpha &=\frac{2}{\sqrt{5}}, & \sin\alpha =\frac{1}{\sqrt{5}} \\\rightarrow \tan\alpha &=\frac{1}{2}&&\\&\therefore \text{C.}\end{aligned}

Question 2
HSC 2016 - Question 7 (External Link) Show Question
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Question 3
HSC 2018 - Question 11c (External Link) Show Question
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Question 4
HSC 2015 - Question 11d (External Link) Show Question
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