W ARM UPM AY 14 TH The equation models the height of the tide along a certain coastal area, as compared to average sea level (the x-axis). Assuming x =

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Trigonometric Functions

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W ARM UPM AY 14 TH The equation models the height of the tide along a certain coastal area, as compared to average sea level (the x-axis). Assuming x = 0 is midnight; use the graph of the function over a 12-hour period to answer the following questions. 1. What is the maximum height of the tide? 2. When does it occur? 3. What will the height of the tide be at 11 A.M.? 4. When will the height be 6 feet below sea level?

H OMEWORK C HECK /Q UESTIONS ? 1. y = 2cos(π/2 x)y = -3sin(2x) y = -3cos(1/2 x) a) (0, 6), (0.5, 10) and (1, 6) (0, 6), (30, 10) and (60, 6) b) Period = 1 minute, Amplitude = 2 OR Period = 60 seconds c) y = -2cos(2πx) + 8 OR y = -2cos(π/30 x) a) calc. set window  x: 0 – 24, y: b) 78° c) t =.979 and  during January

T RIG T RASHKETBALL

N O C ALCULATOR 1. Sin(π/2) 2. Cos(510°) 3. Csc(7π/6) 4. Sec(180°) 5. Tan(5π/3) 6. Cot(3π/2) 7. Sin(360°) 8. Cos(3π/4) 9. Csc(120°) 10. Sec(7π/4) 11. Tan(270°) 12. Cot(-240°)

N O C ALCULATOR Give the values of angles in radians such that 0 < x < 2π for which the given value is true. 1. Sinx = 0 2. Cosx = -√3/2 3. Tanx = 1

N O C ALCULATOR Give the values of angles in radians such that 0 < x < 2π for which the given value is true. 1. 4sinx + 2 = = 2cos 2 x + 1

N O C ALCULATOR y = 3sin(πx) – 5 Amplitude = Period = Interval = Horizontal Shift = Vertical Shift =

N O C ALCULATOR Amplitude = Period = Interval = Horizontal Shift = Vertical Shift =

N O C ALCULATOR Match each graph to the correct function. 1. y=sinx 2. y=cosx 3. y=-sinx 4. y=-cos x A.B. C.D.

C ALCULATOR A CTIVE 1. Find the point (x, y) on the unit circle that corresponds to t = -7π/6 2. Find 4 coterminal angles (2 positive and 2 negative) for -7π/9  answer in radians (do not convert to degrees!)

C ALCULATOR A CTIVE 1. Determine the quadrant in which the terminal side of the angle 8π/5 lies. 2. Determine the quadrant in which the terminal side of the angle 572  lies.

C ALCULATOR A CTIVE In which quadrant is an angle if… 1. sinx 0 2. cosx > 0 and cscx > 0 3. cotx 0

C ALCULATOR A CTIVE Simplify each expression using identities: 1. 1 – cos 2 x 2. (sinx)(secx)

C ALCULATOR A CTIVE Simplify the expression using identities:

C ALCULATOR A CTIVE The point (8,-3) is on the terminal side of an angle  in standard position. Sketch a picture and find the value of each of the following. 1. cosθ = 2. cscθ = 3. cotθ =

C ALCULATOR A CTIVE Change degrees to radians and radians to degrees °2. 11π/4

C ALCULATOR A CTIVE State the measure of the reference angle °2. 9π/14

C ALCULATOR A CTIVE Find an angle between 0° and 360° or 0 and 2  which is co-terminal with the angle given °2. -2π/3 (answer in radians)

C ALCULATOR A CTIVE Write an equation for the graph.