Determining trigonometric functions given their graphs

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  1. For the following graph, write an equation (with the smallest phase shift) in the form of:
    (i) y = a sin b(x - c) + d
    (ii) y = - a sin b(x - c) + d
    (iii) y = a cos b(x - c) + d
    (iv) y = - a cos b(x - c) + d

    1. Determining trigonometric functions given their graphs

    2. writing the trigonometric equations according to their graphs
  2. A sinusoidal curve has a minimum point at (π3,  5)\left( { - \frac{\pi }{3},\; - 5} \right) and the closest maximum point to the right is (  π6,  3)\left( {\;\frac{\pi }{6},\;3} \right). Determine an equation of this curve.