1 / 22

Trigonometric Functions Review: Amplitude, Period, & Principal Axis for Success!

Prepare for your trigonometry test with this comprehensive review! Gain a solid understanding of key concepts such as amplitude, period, and principal axis, illustrated through engaging examples. You’ll learn to determine the amplitude from the equation, find the period with a simple calculation, and identify the principal axis for sine and cosine functions. Complete exit slips will help test your knowledge and ensure you're ready for the exam. Let's ace this together!

rangle
Download Presentation

Trigonometric Functions Review: Amplitude, Period, & Principal Axis for Success!

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. Trigonometric Functions Review The test is tomorrow! You will do awesomely! Yay!

  2. Example 1: Roller Coaster Height

  3. Finding info from the equation 5 min lesson, 5 min exit slip!

  4. Amplitude The number in front of sin or cos is the amplitude. If there is no coefficient, it is 1. Ignore negative/positive sign. Amplitude is distance, so it is always positive. Amplitude for this equation = 3

  5. Period The number in front of the x (inside the parentheses) is our clue to the period. If there is no coefficient, the clue number is 1. To find the period, divide: 360/clue In this case, we get: 360/2 = 180º

  6. Principal Axis The number added or subtracted is the principal axis – the vertical shift. We write the principal axis as an equation: Here, the answer is: Y = 2

  7. Review All Together Period Clue Principal Axis Amplitude Amplitude = 3 Period = 360/2 = 180º Principal Axis: y = 2

  8. Exit Slip!!! 3 minutes! • Write down the: • Amplitude • Period • Principal Axis Answers: Amplitude = 4, Period = 360/3 = 120º, Principal Axis: y = -2

  9. Graphing Sine and Cosine Equations 10 min lesson, 8 min exit slip!

  10. Determine the View Window (calc.) You should always be able to answer these 6: Xmin: 0º (start) Ymin: 2 – 3 = -1 Xmax: 360º (finish) Ymax: 2 + 3 = 5 Xscl: 90º (always) Yscl: 1

  11. Graph it on your calculator (degrees)

  12. Graph it on paper! • You should do the following: • Draw your principal axis • Sketch the min and max lines • Sine starts in the middle, Cos starts at the maximum

  13. Determine the View Window (calc.) Amplitude = 2, Period = 360º, Pr. Axis: y = -3 You should always be able to answer these 6: Xmin: 0º (start) Ymin: -3 – 2 = -5 Xmax: 720º (finish) Ymax: -3+ 2 = -1 Xscl: 90º (always) Yscl: 1

  14. Graph it on your calculator (degrees)

  15. Exit Slip!!! 3 minutes! Sketch the graph of the one above for: 0º ≤ x ≤ 360º !! Answer Graph:

  16. Solve Trig. Equations 5 min lesson, 4 min exit slip!

  17. Determine the View Window (calc.) Xmin = 0, xmax = 360, xscl = 90 Ymin = -5, ymax = -1, yscl = 1 Y1 = -2cos(x) – 3 Y2 = -2 2nd-Trace-Intersect

  18. Determine the View Window (calc.) Answers: 120º, 240º

  19. Solve for x (should have multiple answers) for 0º ≤ x ≤ 360º! Exit Slip!!! 3 minutes! • 6 Answers: 9.65º, 110º, 130º, 230º, 250º, 350º • Explanation: • I have to give 3 significant figures for each. • Another way: 9.65 and 110º happen in the first cycle. • Because the period is 120º, add 120º to each to get 130º and 230º. • Then add 120º again to each to get 250º and 350º.

  20. Real-Life Trig Problems 5 min lesson, 4 min exit slip!

  21. Temperature: Find amplitude, period, pr. Axis and write eq. Amplitude = (16 – 7)/2 = 4.5 Period = 12 months Pr. Axis: average y: (16 + 7)/2 = 11.5

  22. Depth: Find amplitude, period, pr. Axis and write eq. 1.5 30 4.5 Period = 360/b 12 = 360/b B = 30 (check: 12*30 = 360) Vertical translation = principal axis, the middle (average of max and min) = (6 + 3)/2 = 4.5 Amplitude = ½ the distance between max & min A = (6 – 3)/2 = 1.5

More Related