Essential Question:

13-4: The Sine Function Recall: the sine of Θ is the y-value where an angle intersects the unit circle. Important things to note: The curve starts at 0 The curve begins going up, and returns to 0 halfway through the cycle (at 180˚) The curve reaches a maximum of 1 (at 90˚) and a minimum of -1 (at 270˚) 90˚ 180˚270˚360˚0˚0˚

13-4: The Sine Function Finding the period of a Sine Curve Use the graph of y = sin 4Θ below How many cycles occur in the graph? 4 Find the period of y = sin 4Θ Take the period of the parent function Divide the interval by the number of cycles 2   4 =  / 2 Alternately: Divide the parent period by the number in front of the theta Parent period for sin/cos is 2  22

Find the period of each sine curve below. 2222 2  2  / 3

13-4: The Sine Function Finding the Amplitude Same as in Chapter 13-1 The amplitude is half the difference between the maximum and minimum values of the function. Find the amplitude of each sine curve below 4 3

13-4: The Sine Function Properties of Sine Functions y = a sin bΘ |a| is the amplitude b is the number of cycles from the interval 0 to 2 2 / b is the period of the function

13-4: The Sine Function Assignment Page 738 – 739 Problems 1 – 15, (odds) For problems 23 – 27, don’t sketch the graph Instead, tell me the amplitude and period of the function given.