10.2N – Graphing Sine and Cosine A. Graph Sine and Cosine

Parent sine graph 𝑓(𝜃) = sin𝜃 Parent cosine graph 𝑓(𝜃) = cos𝜃 Draw the graph and make a table. Draw the graph and make a table.

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B. Transformations 1. From the 4 transformations in 9.1, today we are discussing _____________ and _______________.

2. What is the general equation for a trigonometric function? __________________________________

Phase shift and Period:

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3. Which variable in the equation is related to a horizontal shift? ________ • In the parent graph this is: ______

4. Which variable in the equation is related to a horizontal stretch? ________

• In the parent graph this is: ______ • This is used to find the period. The formula for period is: ____________ • The period in the parent graph is ______________

5. Frequency is defined as the number of oscillations or rotations per unit of time.

• Frequency is the reciprocal of the period. The formula for frequency is __________ • The frequency in the parent graph is _________

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D. Making the Graph. (Phase Shift and Period) EX. 1) 𝑓(𝜃) = sin(𝜃 + 𝜋)

Phase Shift_____ b____ Period_____ Freq._____

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EX. 2) 𝑓(𝜃) = cos�𝜃 − 𝜋4�

Phase Shift_____ b____ Period_____ Freq._____

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EX. 3) 𝑓(𝜃) = cos 2𝜃

Phase Shift_____ b____ Period_____ Freq._____

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EX. 4) 𝑓(𝜃) = sin 𝜃4

Phase Shift_____ b____ Period_____ Freq._____

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EX. 5) 𝑓(𝜃) = −sin 2(𝜃 − 𝜋)

Phase Shift_____ b____ Period_____ Freq._____

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EX. 6) 𝑓(𝜃) = cos 3 �𝜃 + 𝜋3�

Phase Shift_____ b____ Period_____ Freq._____

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