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. Ignore negative/positive sign. Amplitude is distance, so it is always positive. Amplitude for this equation = 3

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

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

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

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

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

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

Graph it on your calculator (degrees)

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

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

Graph it on your calculator (degrees)

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

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

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

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

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.

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

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

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