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Trigonometric Functions Review

Trigonometric Functions Review. The test is tomorrow! You will do awesomely! Yay!. Example 1: Roller Coaster Height. Finding info from the equation. 5 min lesson, 5 min exit slip!. Amplitude. The number in front of sin or cos is the amplitude. If there is no coefficient, it is 1.

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Trigonometric Functions Review

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  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

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