1. Do Now quick Summary Sheet Quiz Due at 2:20 pm As a freshman, you invest $3,000 in a bank account that yields 5.5% interested compounded quarterly. 5 years at Hyde how much $ will you have? HYPER MATH

2. UNIT 5 TRIGONOMETRY Class One: Degrees  Radians Radian Unit Circle Do Now Convert to Degrees Measure: π/4= 3π/2= π/6 = Convert to Radian Measure {keep π} 330 = 285= 92 = Homework: page 352 – 353 #’s35,41,49,55,63,67, 77* To convert from radians to degrees, multiply the angle by 180/ π To convert from degrees to radians, multiply the angle by π/180

3. UNIT CIRCLE Unit Circle Degree --> Radian

4.  Do Now:  IF f (x) = 2x 2 + 2x - 3  Find the Roots and Vertex  Page 352-53 #47, #57  Homework  Page 35377, 79, 91 – 98 all#99

5.  Coterminal Angles have the same  INITIAL SIDE  TERMINAL SIDE  Example 2 page 343 For example 30°, –330° and 390° are all Coterminal.

6.  Page 344 example 4/ Example 5  60 minutes / degree  60 seconds / minute  3600 seconds / degree  Convert 45.65 to deg-min-sec  Convert 65° 35’ 22” to degree decimal

7.  Arc Length (s) = α * r  Θ  degrees  α  Radian  Arc Length (s) = α * r  Arc Length (s) = Θ *{π/180} * r  Example 9 Page 349  Find the distance a mountain bike wheel covers after (1) revolution? {mountain bike tires are typically 26” in diameter}

8. Class Three Arc Lengths Linear Velocity Angular Velocity {Distance / Area } Do Now ◦ Find and graph the linear equation that goes through ◦ the points (3, 5) and ( 5, 10) ◦ Page 353 #91 Find the Arc Length if  α = π/4 and the radius is 12 feet Homework Page 349Examples 9 and 10 ◦ Page 354 #, 99, 100, 103, 104, 113, 114, ◦ 105 – 109

9. Linear Velocity Example 11 Angular Velocity Example 12 Angular Velocity = Angle / time = Radians /sec = Degrees / sec ω = α / t Linear Velocity = distance / time = meters /sec = ft / sec V = s / t

10. Class FOUR Word Problems Arc Lengths Linear Velocity Angular Velocity In Class The average radius of the Earth, or the distance from the center to surface is 6,371 km, or 3,959 miles. But wait, the answer is actually a little more complicated than that. As you probably know, the Earth is rotating on its axis, completing one full revolution in just less than 24 hours. This relatively rapid rotation causes the Earth’s poles to flatten, and our planet bulges at the equator. Instead of a perfect sphere, the Earth is a flatted sphere. This means that the distance from the center to the equator is further than the distance from the center to the Earth’s poles. The equatorial radius of the Earth is 6,378.1 km, and the polar radius of the Earth is 6,356.8 km. Subtract those two numbers and you get 21.3 km. In other words, points on the equator are actually 21.3 km further from the center of the Earth than the poles. Find the distance from Rio de Janeiro [22º 54' 10" S] to Miami Florida [ 25° 46' 26" N ] u sing the average radius of Earth In Class  Homework Page 349Examples 9 and 10 Page 354 #, 102, 105 – 109, 110, 111, HONORS #’s Page 354 #, 99, 100, 103, 104, 113, 114, Do NOW What is the length of the crust of 2 slices from a 20” pizza cut into 10 EQUAL pieces? What is the AREA of the 2 pieces?

11. DO NOW page 356 pop quiz # 1 – 7 all In Class  WORK TOGETHER TO SOLVE ALL THE Homework PROBLEMS Page 349Examples 9 and 10 Page 354 #, 102, 105 – 109, 110, 111, HONORS #’s 115, 116 Page 354 #, 99, 100, 103, 104, 113, 114, TUESDAY TEST on Page 353 any of the problems

12. Day Five Word Problems Angular and Linear Velocity Basic SIN and COS Do Now: Find the COS ( α) of α = 9π/2 =__________ Convert 600 degrees into Radians and find the COS of the radian measure. =________________ Find the ARC Length if α = π/4 and r = 12ft =_______ Solve for x if 3 x = 7x = _____________ Homework: Reference Angle – page 361 Example 4 Fundamental Identity – page 36 Example 7 Page 366 For Thought 1 – 10 ALL

13. DO NOW Page 354 # 106Linear Velocity In Class Page 354 # 108Angular Velocity Page 354 # 110Linear Velocity with trig Page 354 # 113Area of a circle sector Page 356 Linking Concepts 20 meter Ferris wheel a  c Reference Angle – page 361 Example 4 Fundamental Identity – page 364 Example 7 Homework CHANGE pg 354 – 355 101 – 113 ODD Summary Sheet for Quiz Conversion Arc Lengths Day Five Word Problems Feb 3 2011 Angular and Linear Velocity

14. DO NOW: Find the radius of a circle whose ARC Length is 10 Feet and the central angle is π/12 radians= Last Nights Homework CHANGE pg 354 – 355 101 – 113 ODD 115 and 116 ALL or NOTHING Summary Sheet for Quiz Conversion Arc Lengths IN CLASS TODAY (Friday) Graphing SIN and COS

15.  Do Now: Find the SIN and COS of the following to four decimal places: Example 1 page 357 Θ= 33° Sin = ____ Cos = ____ Θ= 123° Sin = ____ Cos = ____ Θ= 333° Sin = ____ Cos = ____ α = 3π SIN = ___ COS = ___ α = 3π/2 SIN = ___ COS = ___ α = 4π/3 SIN = ___ COS = ___ In class – Homework Know the 1 st quadrant SIN COS for Primary Angles 0 – 30 – 45 – 60 – 90 0 - π /6- π /4 - π /3 - π /2 MAKE YOUR Degree Wheel Page 361 Example 4 Reference Angle Page 366 For Thought 1 – 7 Page 366 – 367 #’s 7 – 15 ODD29 – 35 ODD

16.  IN CLASS  Homework  Motion of a spring Example 8 Page 365  Word Problems Page 367 #’s 95 – 100  Pop Quiz page 368 1 – 8 ALL

17. Day Eight: Graphing Amplitude Period Shift {Phase Shift} Do Now: On your Calculator - graph {in Radians} Y = SIN(X) Y = COS (X) Y = COS (X – π/2) IN CLASS: Graph Y = 4 SIN (X) Graph Y = 4 SIN(2X) Graph Y = 4 SIN (X) +3 Fundamental SIN Equation  f(x) = A SIN{Bx} + D

18. Trigonometry - Graphing Plot the equations for a SIN or COS function a) f (x) = D + A SIN (B {x – C}) D = shift on the “Y” axis= {MAX + MIN} /2 A = Amplitude= {MAX – MIN} /2 B finds the period of the cycle = 2π / B If B = 1 then the “normal” period is 2π (a circles circumference) C = shift on the “X” axis Day Eight: Graphing

19. Homework: {Page 381} #’s 1 – 4 ALL GRAPH - #’s 5, 6, 15, 16, 21, 23 Graph the equation f( α ) = Y = 2 + 4 * SIN ({1/4} α )

20.  Physics Oscillations - Simple Harmonic Motion = SINE WAVES Physics Oscillations - Simple Harmonic Motion = SINE WAVES  f (x) = D + A SIN (B {x – C})  Simple Haronic Motion EQUATIONS Simple Haronic Motion EQUATIONS  X(t) = A Sin ( ωt + ф)  F(x) = -kx  Homework Pg 383 77-85 ODD

21.  If the frequency of a sound wave (SIN wave) is 40,000 cycles per second (Hz).  a)What is the period?  b)If the Amplitude is 5.5 what is the SIN equation that governs the sound wave?

22.  Homework:  Page 384 – 385 #86,87,91,93

23. Day 11 Review Do Now: #1 CLEAN THE ROOM #2If a company experiences its maximum sales ($40,000) in December and its lowest sales in June ($10,000), write the trigonometric equation if December is month zero and t= the # of months after December.

24. Day 11 Review Angles Velocities What is the reference angle for 120 degrees? = What is the exact value for Sin (3π/4) = What is the value of: Sin 2 (37π/42) + Cos 2 (37π/42) = What is the linear velocity of the second hand of the clock in room one if the second hand has a length of 3” in ft/sec = What is the angular velocity of the minute hand of the clock in room one if the minute hand has a length of 5” in ft/sec =

25. Day 12 TEST Homework Basic Trigonometric Functions Tangent Cotangent Secant Cosecant Page 396 #’s 1 – 6 all Page 397 #’s:3,5,7,11,15,29, 31,33,35 Honors #51

26. Day 13 Group B and E Group B Group E Linear- Quadratic Reference – Coterminal Angular – Linear Velocities Graph SIN – COS f(x) = D+A*SIN(Bx) Homework : Page382 #’s 41 – 47 ODD Linear- Quadratic Reference – Coterminal Angular – Linear Velocities Graph SIN – COS – Graph TANGENT Homework Page 386 #’s 1-5 ALL Page 397 #’s 51,52,57,58, 63, 64

27. Day 14A (Feb 16)Group B and E Day 14 Graph SIN – COS f(x) = D + A*SIN(B*x) In-Class /Homework Page 382 #’s 55, 59, 60, 62 Linear- Quadratic Reference – Coterminal Angular – Linear Velocities Graph SIN – COS – Graph TANGENT Recognize COT – SEC - CSC In-Class /Homework Page 392 Examples 4, 5, 6, Page 396 Gallery Page 398 #’s 83 – 92 Honors 97 Group B Do Now Graph f(x) = 5 + 2Sin (2 {x}) Group E Do Now Graph f(x) = 5 + Tan(2 {x + π/2})

28. Day 14B (Feb 17)Group T= Travel Lane and F = Fast Lane Linear- Quadratic Reference – Coterminal Arc Length s = α r Angular – Linear Velocities page 350 ω = α/t v =s /t = 2πr/t = αr/t v = r*ω In-Class /Homework Page 349 - 351 Examples 9 - 10 - 11 Page 354- 355 #’s 103, 104. 107, 108, 111 Linear- Quadratic Reference – Coterminal Angular – Linear Velocities Graph SIN – COS – Graph TANGENT Recognize COT – SEC - CSC In-Class /Homework Page 392 Examples 4, 5, 6, Page 396 Gallery Page 398 #’s 83 – 92 Honors 97 Graph COT – SEC – CSC Find: SIN -1 – COS -1 – TAN -1 ArcSIN – ArcCOS = ArcTAN In-Class /Homework Page 403 example 5, 6, 7, 8 Page 408 #’s 1 – 35 ODD<3 Group T Do Now Graph f(x) = 3.5 + 5*Sin (1/2 {x}) Group F Do Now Graph f(x) = 3.5 + Tan(1/2 {x})

29. Day 15 Feb 18 Group F Do Now Group T Do Now Linear- Quadratic Reference – Coterminal Graph SIN – COS f(x) = D + A*SIN(B*x) Arc Length s = α r Angular – Linear Velocities page 350 ω = α/t v =s /t = 2πr/t = αr/t v = r*ω In-Class /Homework Page 349 - 351 Examples 9 - 10 - 11 Page 354- 355 #’s 103, 104. 107, 108, 111 MONDAY Graph TANGENT page 389-390 f(x) = D + A*Tan (Bx) P = π/B (NOT 2 π/B ) In-Class /Homework Page 389 example 2 391 gallery Page 397#’s 51, 52, 57, 58, 63, 64 Linear- Quadratic Reference – Coterminal Angular – Linear Velocities Graph SIN – COS – Graph TANGENT Graph COT – SEC – CSC Find: SIN -1 – COS -1 – TAN -1 ArcSIN – ArcCOS = ArcTAN In-Class /Homework Page 403 example 5, 6, 7, 8 Page 408 #’s 1 – 35 ODD Page 420 43 – 49 ODD NEW STUFF USING TRIG!!!

30. Monday Presidents Day Group F: Do Now: Which Presidents does Presidents Day HONOR? Group T  RETAKE TEST Non Right Triangles Page 510 & 520 #’s 5 – 19 ODD Homework MONDAY Graph TANGENT page 389-390 f(x) = D + A*Tan (Bx) P = π/B (NOT 2 π/B ) In-Class /Homework Page 389 example 2 391 gallery Page 397#’s 51, 52, 57, 58, 63, 64 LAW of COSINE c 2 = a 2 + b 2 – 2ab*COS C b 2 = a 2 + c 2 – 2ac*COS B a 2 = c 2 + b 2 – 2cb*COS A LAW of SINE SIN (<A) / a = SIN (<B) / b = SIN (<C) / c  where :a, b, and c are SIDES OPPOSITE Angles <A, <B, and <C

31. TUESDAY Feb 22 Group F: Do Now: Find all 3 angles and 3 Sides If Side a = 4 b= 7 c=? <A = 55 <B= ? <C =? Group T  MALI Willie and GABI RETAKE TEST Non Right Triangles Homework CHECK Page 510 & 520  #’s 5 – 19 ODD LAW of SINE SIN (<A) / a = SIN (<B) / b = SIN (<C) / c  where :a, b, and c are SIDES OPPOSITE Angles <A, <B, and <C In Class Page 511 #31 – 39 ODD Homework TUESDAY IN CLASS Graph TANGENT page 389-390 f(x) = D + A*Tan (Bx) P = π/B (NOT 2 π/B ) In-Class /Homework Page 389 example 2 391 gallery Page 397#’s 51, 52, 57, 58, 63, 64 LAW of COSINE c 2 = a 2 + b 2 – 2ab*COS C b 2 = a 2 + c 2 – 2ac*COS B a 2 = c 2 + b 2 – 2cb*COS A NEW Heron’ s Rule : Area = √{s* (s-a) (s-b)(s-c)} Where s = ½ * ( a + b + c)

32. Day 16 Group T and F Group F Group T Linear- Quadratic Reference – Coterminal Angular – Linear Velocities Graph SIN – COS f(x) = D + A*SIN(B*x) Graph TANGENT page 389-390 f(x) = D + A*Tan (Bx) P = π/B (NOT 2 π/B ) In-Class /Homework Page 389 example 2 391 gallery Page 397#’s 51, 52, 57, 58, 63, 64 Page 387 Recognize COT ( Θ) – SEC ( Θ) – CSC ( Θ) COT ( Θ) = 1 / TAN ( Θ) SEC ( Θ) = 1/ COS ( Θ) CSC( Θ) = 1/ SIN( Θ) Linear- Quadratic Reference – Coterminal Angular – Linear Velocities Graph SIN – COS – Graph TANGENT Recognize COT – SEC – CSC Find: SIN -1 – COS -1 – TAN -1 ArcSIN – ArcCOS = ArcTAN MORE USING TRIG

33. Fast Lane - Vectors Homework – Summary Sheet

34. Travel Lane – SOH CAH TOA FINDING THE SIDES Homework – Summary Sheet Given a Right Triangle with one angle and one side Find the missing angles and missing side A 2 + B 2 = C 2  Adj 2 + Opp 2 = Hyp 2 SIN θ = Opp/ Hyp SOH COS θ = Adj/ HypCAH TAN θ = Opp/ Adj TOA Hyp Opp Θ Adj

35. Finding the ANGLES Given a right triangle three sides Find the missing angles ARCSIN (Opp / Hyp ) = θ ARCCOS (Adj / Hyp ) = θ ARCTAN (Opp / Adj ) = θ Sin 30 = ½ ARCSIN (1/2) = 30 Degrees Sin 45 =.7071 ARCSIN (o.7071) = 45 degrees

36. b C A B c a C= 90A = 40B = ___ c = 10 a = ___b = ___ C= 90A = 30B = ___ c = __ a = 10b = ___ C= 90A = ___ B = ___ c = 10 a = 6.4278 b = ___ C= 90A = ___B = ___ c = 20 a = 10b = ___