Concept Byte: Graphing Trigonometric Functions

For Use With Lesson 13-4

TECHNOLOGY

Activity 1

Compare the graphs of y = cos x y equals cosine x  from − 360 ° negative 360 degrees  to 360° and from − 2 π negative 2 pi  to 2 π  radians . 2 pi , radians , .

• Step 1 Press mode begin box , mode , end box  to set the mode to degrees. Adjust the window values. Graph the function.

  
  Image Long Description

• Step 2 Change the mode to radians. Graph the function.

  

The graphs appear to be identical. The function has a period of 360° or 2π radians.

Activity 2

Graph the function y = sin x . y equals sine x .  Find sin 30° and sin 150°.

• Step 1 Set the mode to degrees and adjust the window values as shown.

  

• Step 2 Graph the function. Use the trace begin box , trace , end box  key to find the y-values when x = 30 x equals 30  and x = 150 . x equals 150 .

  

Exercises

Use appropriate window values to identify the period of each function in radians and in degrees. Then evaluate each function at 90°.

1. y = cos x y equals cosine x
2. y = sin x y equals sine x
3. y = sin 3 x y equals sine 3 x
4. y = − 3 sin x y equals negative 3 sine x
5. y = cos ( x + 30 ) y equals cosine open x plus 30 close

Writing Graph the two functions in the same window. Compare the graphs. How are they similar? How are they different?

6. y = sin x , y = cos x y equals sine x comma y equals cosine x
7. y = sin x ,  y = cos ( x − π 2 ) y equals sine x comma . y equals cosine . open . x minus , pi over 2 . close
8. y = sin x ,  y = cos ( x + π 2 ) y equals sine x comma . y equals cosine . open . x plus , pi over 2 . close

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