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Graph the following in your calculator. Find the period and minimum and maximum values for each function. O 1. f(x) = sin θ O 2. f(x) = cos θ 12.7 Graphing Trigonometric Functions Sine, Cosine and Tangent 𝑜𝑟 2𝜋 𝑜𝑟 2𝜋 The amplitude of the graph of sine and cosine functions equals half The difference between the maximum and the minimum values. 𝑜𝑟 2𝜋 𝑏 Finding Amplitude and Period Example 1a O Find the amplitude and period of O 𝒚= 𝟏 𝒔𝒊𝒏 𝜽 𝟑 Example 1b O Find the amplitude and period of O 𝒚 = 𝟐𝒄𝒐𝒔 𝟓𝜽 Example 2 𝟏 O Graph the function y = 𝟐 O First, find amplitude and period O Graph θ y θ y sin . (Radians) Example 3 O Graph the function y = cos 3. (Degrees) O First, find amplitude and period O Graph θ y Example 4 O Graph the function y = 2 sin O First, find amplitude and period O Graph θ y 𝟏 . 𝟐 (Radians) Example 5 O Graph the function y = 4 cos 𝟐. (Degrees) O First, find amplitude and period O Graph θ y Example 6 𝟏 Find the period of 𝒇 𝒙 = 𝐭𝐚𝐧 𝜽. Then graph the 𝟐 function in radians. Example 7 O Find the period of y = tan 2. Then graph the function in degrees. Applications Example 8 O Humans can hear sounds with a frequency of 40 Hz. Find the period of the function that models the sound waves. O Let the amplitude equal 1 unit. Write a sine equation to represent the sound wave y as a function of time t. Example 9 O A boat on a lake bobs up and down with the waves. The difference between the lowest and highest points of the boat is 8 inches. The boat is at equilibrium when it is halfway between the lowest and the highest points. Each cycle of the periodic motion lasts 3 seconds. Write an equation for the motion of the boat. Let h represent the height in inches and let t represent the time in seconds. Assume the boat is at equilibrium at t = 0 seconds.