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Trigonometry – My Grandmother Also Can Do This!

Tuition given in the topic of E-Maths Tuition Questions from the desk of Miss Loi at 5:39 pm (Singapore time)

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Today’s question looks sooo simple. Just punch those keys on your state-of-the-art Casio scientific calculator and you will get it right … except that this is a Paper 1 question and your favourite Casio calculator should not be there!

So how now? Go ask your Grandma (Ah SOH) with the big foot (TOA CAH) for help lah!

Diagram for this question In the diagram, a ladder BC is leaning against the wall AD. Given that, sin x = 5/13. Find the cosine of angle DCB.


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  1. Nick's Avatar
    Nick commented in tuition class


    sin x = 5/13 => sin ABC = 5/13 => cos BCA = 5/13 => cos DCB = -5/13.

  2. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    Great stuff Nick!

    The purpose of this question is to remind students that the standard trigo ratios (i.e. TOA CAH SOH -> Tan: Opp/Adj; Cos: Adj/Hypo; Sin: Opp/Hypo) applies only to an acute angle.

    In order to solve for angle DCB which is an obtuse angle in the question, students need to remember a further set of equations i.e:

    sin θ = sin (180o - θ)
    cos θ = -cos (180o - θ)
    tan θ = -tan (180o - θ)

    Hence exam questions usually require multiple steps like these. If everyday just simply TOA CAH SOH TOA CAH SOH, the examination board can close shop liao!

    So remember this well!

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