1 / 13

Day 49: Graphs of Secant and Cosecant

Day 49: Graphs of Secant and Cosecant. Plan for the Day. Review Homework Secant and Cosecant Homework Next time: Quiz on Graphing Sine and Cosine (including bx – c). x. 0. cos x. 1. 0. -1. 0. 1. y = cos x. y. x. Graph of the Cosine Function. Cosine Function.

yoshi-mcfarland
Download Presentation

Day 49: Graphs of Secant and Cosecant

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Day 49:Graphs of Secant and Cosecant

  2. Plan for the Day • Review Homework • Secant and Cosecant • Homework • Next time: Quiz on Graphing Sine and Cosine(including bx – c)

  3. x 0 cos x 1 0 -1 0 1 y = cos x y x Graph of the Cosine Function Cosine Function To sketch the graph of y = cos x first locate the key points.These are the maximum points, the minimum points, and the intercepts. Then, connect the points on the graph with a smooth curve that extends in both directions beyond the five points. A single cycle is called a period.

  4. x 0 sin x 0 1 0 -1 0 y = sin x y x Graph of the Sine Function Sine Function To sketch the graph of y = sin x first locate the key points.These are the maximum points, the minimum points, and the intercepts. Then, connect the points on the graph with a smooth curve that extends in both directions beyond the five points. A single cycle is called a period.

  5. Key Steps in Graphing Sine and Cosine Identify the key points of your basic graph • Find the new period (2π/b) • Find the new beginning (bx - c = 0) • Find the new end (bx - c = 2π) • Find the new interval (new period / 4) to divide the new reference period into 4 equal parts to create new x values for the key points • Adjust the y values of the key points by applying the change in height (a) and the vertical shift (d) • Graph key points and connect the dots

  6. Get out your graphing calculator… Graph the following y = cos x y = sec x What do you see??

  7. The graph y = sec x, use the identity . y Properties of y = sec x 1. domain : all real x x 4. vertical asymptotes: Graph of the Secant Function Secant Function At values of x for which cos x = 0, the secant function is undefined and its graph has vertical asymptotes. 2. range: (–,–1]  [1, +) 3. period: 2

  8. First graph: • y = 2cos (2x – π) + 1 Then try: • y = 2sec (2x – π) + 1

  9. Graph Graph the following y = sin x y = csc x What do you see??

  10. To graph y = csc x, use the identity . y Properties of y = csc x 1. domain : all real x x 4. vertical asymptotes: Graph of the Cosecant Function Cosecant Function At values of x for which sin x = 0, the cosecant functionis undefined and its graph has vertical asymptotes. 2. range: (–,–1]  [1, +) 3. period: 2 where sine is zero.

  11. First graph: • y = -3 sin (½x + π/2) – 1 Then try: • y = -3 csc (½x + π/2) – 1

  12. Key Steps in Graphing Secant and Cosecant • Identify the key points of your reciprocal graph (sine/cosine), note the original zeros, maximums and minimums • Find the new period (2π/b) • Find the new beginning (bx - c = 0) • Find the new end (bx - c = 2π) • Find the new interval (new period / 4) to divide the new reference period into 4 equal parts to create new x values for the key points • Adjust the y values of the key points by applying the change in height (a) and the vertical shift (d) • Using the original zeros, draw asymptotes, maximums become minimums, minimums become maximums… • Graph key points and connect the dots based upon known shape

  13. Homework 26 • Page 318:14, 26, 16, 27 • Quiz next time

More Related