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Trigonometry

Trigonometry. Aim # 4-5A: How do we graph variations of sine function?. Here are some values of (x, y) on the graph of y = sin x on the interval 0 < x < 2 π. This is the graph of y = sin x. Remember that one complete cycle for the sine function is 2 π.

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Trigonometry

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  1. Trigonometry

  2. Aim# 4-5A: How do we graph variations of sine function? • Here are some values of (x, y) on the graph of y = sin x on the interval 0 < x < 2π.

  3. This is the graph of y = sin x. • Remember that one complete cycle for the sine function is 2π

  4. This is a more complete graph of y=sin x. Why? • Remember the sine is an ODD function so it has symmetry along the origin.

  5. The graph of y= sin x illustrates the following properties:

  6. Graphing variations of Y = Sinx • To graph a variation of y= sin x remember:

  7. Note when the function reaches its max. and min. points and other key points.

  8. In graphing variation of the sine function, key points can be found by dividing the period into 4 equal parts. • The y-coordinate can be found by evaluating the x-value.

  9. Y = A sinx Ex: y =2 sinx A = 2 We can graph this by multiplying the y-values by 2. A stands for the Amplitude of the function. How do you think the graph of y= sin x will change?

  10. Y= 2 sin x The graph stretched. The range is now [-2,2] instead of [-1,1]. .

  11. Graphing Variations of y= sin x.

  12. Example 1: Graphing a Variation of y= sinx

  13. Example 2:

  14. Graph:

  15. Amplitudes and Periods • If B >1 the graph will shrink by a factor of 1/ B • If 0<B<1 the graph will STRETCH by a factor of 1/B

  16. Example 3:

  17. Now let’s find the 5 key points.

  18. The Graph of y=3 sin 2x

  19. Check for Understanding: 1.Determine the amplitude of y= 3 sinx. Then graph y= sin x and y= 3 sin x for 0< x <2π. 2. Determine the amplitude of y= -1/2 sinx. Then graph y= sin x and y= -1/2 sin x for - π< x < 3π. 3.Determine the amplitude of y= 2 sin 1/ 2x. Then graph for 0< x <8π.

  20. Summary: Answer in complete sentences. • How does the Amplitude affect the graph of y= sin x? • How do you find the period of the sine function? • How does B affect the graph?

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