Harmonic form and trigonometric proof

Harmonic form and trigonometric proof Quiz

Spec 5.6 · Edexcel A-Level Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. Find RR in 5cos⁡x+12sin⁡x=Rcos⁡(x−α)5\cos x+12\sin x=R\cos(x-\alpha).

    • A. 77
    • B. 1313
    • C. 1717
    • D. 169169

  2. 2. Write sin⁡θ−cos⁡θ\sin\theta-\cos\theta as Rsin⁡(θ−α)R\sin(\theta-\alpha) with α\alpha acute (radians).

    • A. 2sin⁡(θ−π4)2\sin\left(\theta-\frac\pi4\right)
    • B. 2sin⁡(θ−π2)\sqrt2\sin\left(\theta-\frac\pi2\right)
    • C. 2sin⁡(θ+π4)\sqrt2\sin\left(\theta+\frac\pi4\right)
    • D. 2sin⁡(θ−π4)\sqrt2\sin\left(\theta-\frac\pi4\right)

  3. 3. Find the minimum value of 3cos⁡θ+4sin⁡θ+13\cos\theta+4\sin\theta+1.

    • A. −4-4
    • B. −5-5
    • C. −6-6
    • D. 11

  4. 4. What is the best first step in proving 1−cos⁡2θsin⁡2θ≡tan⁡θ\dfrac{1-\cos2\theta}{\sin2\theta}\equiv\tan\theta?

    • A. Multiply both sides by sin⁡2θ\sin2\theta
    • B. Replace tan⁡θ\tan\theta by 1cot⁡θ\frac{1}{\cot\theta}
    • C. Replace 1−cos⁡2θ1-\cos2\theta by 2sin⁡2θ2\sin^2\theta and sin⁡2θ\sin2\theta by 2sin⁡θcos⁡θ2\sin\theta\cos\theta
    • D. Square both sides

  5. 5. How many solutions has 3cos⁡θ+4sin⁡θ=63\cos\theta+4\sin\theta=6?

    • A. 22
    • B. 00
    • C. 11
    • D. Infinitely many

Quiz