The R-formula (a cos + b sin)

The R-formula (a cos + b sin) Quiz

Spec E6 · AQA A-Level Maths: Quiz

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  1. 1. Write cos⁡θ+sin⁡θ\cos\theta+\sin\theta in the form Rcos⁡(θ−α)R\cos(\theta-\alpha) with 0∘<α<90∘0^\circ<\alpha<90^\circ.

    • A. 2cos⁡(θ−45∘)\sqrt2\cos(\theta-45^\circ)
    • B. 2cos⁡(θ−45∘)2\cos(\theta-45^\circ)
    • C. 2cos⁡(θ−30∘)\sqrt2\cos(\theta-30^\circ)
    • D. cos⁡(θ−45∘)\cos(\theta-45^\circ)

  2. 2. Find the maximum value of 7sin⁡x−24cos⁡x7\sin x-24\cos x.

    • A. 77
    • B. 2424
    • C. 3131
    • D. 2525

  3. 3. 5sin⁡θ−12cos⁡θ=Rsin⁡(θ−α)5\sin\theta-12\cos\theta=R\sin(\theta-\alpha). Which gives α\alpha?

    • A. tan⁡α=512\tan\alpha=\frac{5}{12}
    • B. tan⁡α=125\tan\alpha=\frac{12}{5}
    • C. tan⁡α=−125\tan\alpha=-\frac{12}{5}
    • D. tan⁡α=135\tan\alpha=\frac{13}{5}

  4. 4. Find the smallest positive θ\theta for which 3cos⁡θ+4sin⁡θ=53\cos\theta+4\sin\theta=5.

    • A. 36.9∘36.9^\circ
    • B. 126.9∘126.9^\circ
    • C. 53.1∘53.1^\circ
    • D. 90∘90^\circ

  5. 5. Find the minimum value of 12cos⁡θ+5sin⁡θ+312\cos\theta+5\sin\theta+3.

    • A. −10-10
    • B. −13-13
    • C. −16-16
    • D. −2-2

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