Average Monthly Temperature, °F Month, x January, 1 36.0 February, 2 39.0 March, 3 46.8 April, 4 56.8 May, 5 66.0 June, 6 75.2 July, 7 79.8 August, 8 78.1 September, 9 71.0 October, 10 59.5 November, 11 49.6 December, 12 39.7 Source: U.S. National Oceanic and Atmospheric Administration

Describe how the graph of the transformed sine function : f(t) = -3 sin(2t) + 1 can be obtained from the "parent" sine wave. Then graph both functions on the graph below; label which is which.

Find an equation for the sinusoidal graph that is shown below. The scale on the x-axis is and the y-axis is 1. Amplitude: Period: Phase Shift: Equation:

11. a) Create a table of values for the function defined by f(0) = cos 0, where 0° ≤ 0 ≤ 360°. Rotation (0) cos ( 0° 30° 60° 90° 1 120° b) Plot these points, and draw a curve. c) Is this a sinusoidal function? Explain. d) Determine the period, the equation of the axis, and the amplitude of the function. Rotation (0) tan 0 e) How does this periodic function compare with the function f(0) = sin 0? 12. a) Create a table of values for the function defined by f(0) = tan 0, where 0° ≤ 0 ≤ 360°. 330° 360° 0° 30° 60° 90° 0 120° ... 330° 360° b) Plot these points, and draw a curve. c) Is this a sinusoidal function? Explain. d) Determine the period, the equation of the axis, and the amplitude of the function.