Using Transformations to Graph the Sine and Cosine

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Using Transformations to Graph the Sine and Cosine Curves • The following examples will

Using Transformations to Graph the Sine and Cosine Curves • The following examples will demonstrate a quick method for graphing transformations of

q. Example 1: Use transformations to graph the following function: • Basic Function:

q. Example 1: Use transformations to graph the following function: • Basic Function:

q. Example 1: Use transformations to graph the following function: • Center Line:

q. Example 1: Use transformations to graph the following function: • Center Line:

q. Example 1: Use transformations to graph the following function: • Reflection in x-axis?

q. Example 1: Use transformations to graph the following function: • Reflection in x-axis?

q. Example 1: Use transformations to graph the following function: • Amplitude: • Four

q. Example 1: Use transformations to graph the following function: • Amplitude: • Four units above and below the center line:

q. Example 1: Use transformations to graph the following function: • Beginning and ending

q. Example 1: Use transformations to graph the following function: • Beginning and ending points of one period:

q. Example 1: Use transformations to graph the following function: • Beginning and ending

q. Example 1: Use transformations to graph the following function: • Beginning and ending points of one period: Length of one period Beginning point (phase shift)

q. Example 1: Use transformations to graph the following function: • Beginning and ending

q. Example 1: Use transformations to graph the following function: • Beginning and ending points of one period: End point Beginning point (phase shift)

q. Example 1: Use transformations to graph the following function: • Begin point •

q. Example 1: Use transformations to graph the following function: • Begin point • End point

q. Example 1: Use transformations to graph the following function: •

q. Example 1: Use transformations to graph the following function: •

q. Example 1: Use transformations to graph the following function:

q. Example 1: Use transformations to graph the following function:

q. Example 1: Use transformations to graph the following function: • Draw the curve

q. Example 1: Use transformations to graph the following function: • Draw the curve through the points.

q. Example 2: Use transformations to graph the following function: • Basic Function:

q. Example 2: Use transformations to graph the following function: • Basic Function:

q. Example 2: Use transformations to graph the following function: • Center Line:

q. Example 2: Use transformations to graph the following function: • Center Line:

q. Example 2: Use transformations to graph the following function: • Reflection in x-axis?

q. Example 2: Use transformations to graph the following function: • Reflection in x-axis?

q. Example 2: Use transformations to graph the following function: • Amplitude: • Three

q. Example 2: Use transformations to graph the following function: • Amplitude: • Three units above and below the center line:

q. Example 2: Use transformations to graph the following function: • Beginning and ending

q. Example 2: Use transformations to graph the following function: • Beginning and ending points of one period:

q. Example 2: Use transformations to graph the following function: • Beginning and ending

q. Example 2: Use transformations to graph the following function: • Beginning and ending points of one period: Length of one period Beginning point (phase shift)

q. Example 2: Use transformations to graph the following function: • Beginning and ending

q. Example 2: Use transformations to graph the following function: • Beginning and ending points of one period: Beginning point (phase shift) End point

q. Example 2: Use transformations to graph the following function: • Begin point •

q. Example 2: Use transformations to graph the following function: • Begin point • End point

q. Example 2: Use transformations to graph the following function: •

q. Example 2: Use transformations to graph the following function: •

q. Example 2: Use transformations to graph the following function:

q. Example 2: Use transformations to graph the following function:

q. Example 2: Use transformations to graph the following function: • Draw the curve

q. Example 2: Use transformations to graph the following function: • Draw the curve through the points.

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