Determining trigonometric functions given their graphs

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Examples

Lessons

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 $\left( { - \frac{\pi }{3},\; - 5} \right)$ $(- \frac{π}{3}, - 5)$ and the closest maximum point to the right is $\left( {\;\frac{\pi }{6},\;3} \right)$ $(\frac{π}{6}, 3)$ . Determine an equation of this curve.

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