# Determining trigonometric functions given their graphs #### Everything You Need in One Place

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