# Determining trigonometric functions given their graphs

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Examples

- 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 - 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.