The t-formulae

The t-formulae Quiz

Spec 1.1–3 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

Each answer is checked as you go, with why.

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  1. 1. If tan⁡θ2=2\tan\frac{\theta}{2}=2, what is cos⁡θ\cos\theta?

    • A. 35\frac35
    • B. 53\frac53
    • C. −35-\frac35
    • D. −53-\frac53

  2. 2. Which expression is tan⁡θ\tan\theta in terms of t=tan⁡θ2t=\tan\frac{\theta}{2}?

    • A. 2t1+t2\frac{2t}{1+t^2}
    • B. 1−t21+t2\frac{1-t^2}{1+t^2}
    • C. 1+t22t\frac{1+t^2}{2t}
    • D. 2t1−t2\frac{2t}{1-t^2}

  3. 3. Substituting the t-formulae into 4cos⁡x+3sin⁡x=14\cos x+3\sin x=1 gives which quadratic?

    • A. 5t2−6t−3=05t^2-6t-3=0
    • B. 5t2+6t−3=05t^2+6t-3=0
    • C. 3t2−6t−5=03t^2-6t-5=0
    • D. 4t2−6t−3=04t^2-6t-3=0

  4. 4. Why must x=πx=\pi be checked separately when using t=tan⁡x2t=\tan\frac{x}{2}?

    • A. tan⁡π=0\tan\pi=0.
    • B. tan⁡π2\tan\frac{\pi}{2} is undefined, so a solution at x=πx=\pi would be lost.
    • C. sin⁡π=1\sin\pi=1.
    • D. t=πt=\pi is not an integer.

  5. 5. What is cosec⁡θ\operatorname{cosec}\theta in terms of t=tan⁡θ2t=\tan\frac{\theta}{2}?

    • A. 2t1+t2\frac{2t}{1+t^2}
    • B. 1−t22t\frac{1-t^2}{2t}
    • C. 1+t21−t2\frac{1+t^2}{1-t^2}
    • D. 1+t22t\frac{1+t^2}{2t}

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