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Section 5.4 More Trigonometric Graphs

Chapter 5 – Trigonometric Functions: Unit Circle Approach. Section 5.4 More Trigonometric Graphs. Cosecant. Graphing y = A csc ( B x - C ) + D. Graph the sine function with dotted lines. The max point of the sine function is the MINIMUM point of the cosecant function.

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Section 5.4 More Trigonometric Graphs

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  1. Chapter 5 – Trigonometric Functions: Unit Circle Approach Section 5.4 More Trigonometric Graphs 5.4 - More Trigonometric Graphs

  2. Cosecant

  3. Graphing y = Acsc(Bx - C) +D • Graph the sine function with dotted lines. • The max point of the sine function is the MINIMUM point of the cosecant function. • The min point of the sine function is the MAXIMUM point of the cosecant function. • Where the sine function and y = D intersect are the vertical asymptotes of the cosecant function.

  4. Cosecant Example • Graph the following equation:

  5. Secant

  6. Graphing y = Asec(Bx- C) + D • Graph the cosine function with dotted lines. • The max point of the cosine function is the MINIMUM point of the secant function. • The min point of the cosine function is the MAXIMUM point of the secant function. • Where the cosine function and y = D intersect are the vertical asymptotes of the secant function.

  7. Secant Example • Graph the following equation:

  8. Tangent

  9. Graphing y = Atan(Bx - C) + D • Find two consecutive asymptotes A pair of consecutive asymptotes occur at • Find the point midway between the asymptotes (this is the x-intercept if there is no vertical shift; the y-value is the D). • Find the points on the graph that are ¼ and ¾ of the way between the asymptotes. These points will have the y-values of D+Aand D-Arespectively.

  10. Tangent Example • Graph the following equation:

  11. Cotangent

  12. Graphing y = Acot(Bx- C) + D • Find two consecutive asymptotes A pair of consecutive asymptotes occur at • Find the point midway between the asymptotes (this is the x-intercept if there is no vertical shift; the y-value is the D). • Find the points on the graph that are ¼ and ¾ of the way between the asymptotes. These points will have the y-values of –A+ D and A+D respectively.

  13. Cotangent Example • Graph the following equation:

  14. Graphing Summary

  15. Graphing Summary

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