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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.