3.7 Circular functions and their graphs

3.7 Circular functions and their graphs Quiz

IB Maths: Analysis and Approaches HL: Quiz

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  1. 1. Find the period of y=2cos⁡(x3)y = 2\cos\left(\frac{x}{3}\right).

    • A. 2π3\frac{2\pi}{3}
    • B. 6π6\pi
    • C. 3π3\pi
    • D. 2π2\pi

  2. 2. Find the range of y=4−3sin⁡xy = 4 - 3\sin x.

    • A. 1≤y≤71 \le y \le 7
    • B. −3≤y≤3-3 \le y \le 3
    • C. −7≤y≤−1-7 \le y \le -1
    • D. 4≤y≤74 \le y \le 7

  3. 3. y=sin⁡xy = \sin x is mapped to y=2sin⁡(x+π4)y = 2\sin\left(x + \frac{\pi}{4}\right). Which transformations are these?

    • A. Vertical stretch factor 2, translation π4\frac{\pi}{4} right
    • B. Horizontal stretch factor 2, translation π4\frac{\pi}{4} left
    • C. Vertical stretch factor 2, translation π4\frac{\pi}{4} left
    • D. Vertical stretch factor 12\frac{1}{2}, translation π4\frac{\pi}{4} left

  4. 4. A Ferris wheel of radius 15 m, centre 18 m above the ground, starts with a seat at the top. Which model fits?

    • A. h=15cos⁡(bt)+18h = 15\cos(bt) + 18
    • B. h=−15cos⁡(bt)+18h = -15\cos(bt) + 18
    • C. h=18cos⁡(bt)+15h = 18\cos(bt) + 15
    • D. h=15sin⁡(bt)+18h = 15\sin(bt) + 18

  5. 5. How many complete cycles does y=sin⁡3xy = \sin 3x complete for 0≤x≤2π0 \le x \le 2\pi?

    • A. 1
    • B. 2
    • C. 3
    • D. 6

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