# Graphing Transformation of Trigonometric Functions

Learning Objectives:

# Understand to Graph Transformations of Trigonometric Functions.

Graphing Transformations of Trigonometric Functions

If we consider Transformations of Sine and Cosine functions then it will be :

and .

Some important features of above equations are :

1.      is the Amplitude.

2.     2π/B is the Period.

3.     C is the Vertical Translation.

·        If C>0, the function is translated up C units.

·        If C<0, the function is translated down  units.

4.     D is the Horizontal Translation.

·        If D>0, the function is translated right D units.

·        If D<0, the function is translated  units to the left.

If we consider Transformations of Tangent and Cotangent functions then it will be :

and

Some salient features of above equations are :

1.     No Amplitude, since there is no maximum and minimum values.

2.     π/B is the Period.

Hook Questions:

1.      What are the definition of Amplitude and Period?

2.      What are the Vertical and Horizontal Translation of Sine and Cosine functions?

3.      Why there is no Amplitude in Tangent function?

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