Ch4.1A – Radian and Degree Measure r

1. Ch4.1A – Radian and Degree Measure r

2. Ch4.1A – Radian and Degree Measure s ~3.14 arcs θ = half circle r θ = 1 radian One radian – the measure of the angle when the arc length = the radius 1 revolution (360˚) = 2π radians (~6.28 arc lengths) ½ revolution ( ) = radians ¼ revolution ( ) = radians 1/3 revolution ( ) = radians 1/8 revolution ( ) = radians

3. Ch4.1A – Radian and Degree Measure s θ r θ = 1 radian One radian – the measure of the angle when the arc length = the radius 1 revolution (360˚) = 2π radians (~6.28 arc lengths) ½ revolution (180˚) = π radians ¼ revolution (90˚) = radians 1/3 revolution (60˚) = radians 1/8 revolution (45˚) = radians

4. Ex1) Find the acute angle equivalent to Ex2) Find the negative angle equivalent to Ex3) Find the positive angle equivalent to

5. Ex4) Find the complement and supplement angles to a) b)

6. Degree/Radian Conversions

7. Degree/Radian Conversions Conversions: Conversion Factor:

8. Ex5) Convert: a) 135˚ b) -270˚ c) d) 2 rad (Quiz on conv in 2 days) Ch4.1A p318 5-19odd,45-55odd

9. Ch4.1A p318 5-19odd,45-55odd Quiz tomorrow! (On conversions)

14. Ch4.1B – Arc Length (Quiz tomorrow!) r

15. Ch4.1B – Arc Length r Length of a circular arc: s = r.θ (θ must be in radians) Ex1) A circle has a radius of 4inches. What is the arc length intercepted by a central angle of 240˚.

16. Linear speed: distance traveled Angular speed: angle swept out time time omega (θ must be in radians) Ex3) The second hand of a clock is 10.2cm long. Find the speed of the second hand.

17. Ex3) A lawn roller is 30in in diameter and makes 1 revolution every 5/6 sec. a) Find the angular speed b) How fast does it move across the lawn?

18. Ch4.1B p319 35-41odd, 52,54,71-81odd,91,95 (Do #35 and #39 in class) (Quiz tomorrow on conversions!)

24. Ch4.1 Quiz Name___________ Convert radians to degrees: A B C D Convert degrees to radians: A B C D 4. 270˚ 4. 90˚ 4. 180˚ 4. 360˚ 5. 60˚ 5. 30˚ 5. 120˚ 5. 150˚ 6. 210˚ 6. 240˚ 6. 330˚ 6. 300˚

25. Ch4.2 – The Unit Circle x2 + y2 = 1 Ex1) 45˚ = _____ rad x = _____ y = _____

26. Ex2) 60˚ = _____ rad x = _____ y = _____ Ex3) 30˚ = _____ rad x = _____ y = _____ Ex5) 90˚ = _____ rad Ex4) 0˚ = _____ rad x = _____ x = _____ y = _____ y = _____

27. Ex6) x = _____ x = _____ y = _____ y = _____ x = _____ x = _____ y = _____ y = _____

28. Trig Functions (sine) (cosine) (tangent) sin t = y cos t = x tan t = Ex7) Eval 3 trigs for: a) b) c) d) Ch4.2A p328 1-39odd (only sin,cos,tan)

29. Ch4.2A p328 1-39odd (only sin,cos,tan)

30. Ch4.2B – Trig Functions sin t = y (cosecant) csct = cost = x (secant) sec t = tan t = (cotangent) cot t = Ex8) Eval 6 trigs for:

31. sin t= ycsct = cost = x sec t = tan t = cot t = Ex9) Eval: a) b)

32. x = costy = sin t Domains: (what you put in for t) Ranges: (what you get out for x or y)

33. Types of functions: 1. x = costis an even function (So is secant) 2. y = sin tis an odd function (So is tan, csc, and cot) Ex10) Use calc: a) sin 76.4˚ (must be in degree mode.) b) cot 1.5 (must be in radian mode.) Ch4.2B p328 57, 2-38 (eoe)

34. Ch4.2B p328 57, 2-38 (eoe)

36. Ch4.3 – Right Triangle Trig SOH-CAH-TOA sin θ = cosθ = tan θ = hypotenuse opposite Θ adjacent

37. Ch4.3 – Right Triangle Trig SOH-CAH-TOA sin θ = cosθ = tan θ = cscθ = sec θ = cot θ = Ex1) Eval 6 trigs for: 5 4 3 hypotenuse opposite Θ adjacent Θ

38. Ch4.3 – Right Triangle Trig SOH-CAH-TOA sin θ = cosθ = tan θ = cscθ = sec θ = cot θ = Ex2) Find the value of sin45˚, cos45˚, tan45˚ hypotenuse opposite Θ adjacent 45˚

39. Ex3) Use the equilateral triangle to find the value of sin60˚, cos60˚, sin30˚, cos30˚

40. Sine, Cosine, and Tangent of Special Angles sin30˚ = cos30˚ = tan30˚ = sin45˚ = cos45˚ = tan45˚ = 1 sin60˚ = cos60˚ = tan60˚ = HW#8) Find exact values of 6 trigs for: 3 6 Ch4.3A p338 1-22(a,b) Quiz tomorrow – would u like 2 c a sample? Θ

41. Sine, Cosine, and Tangent of Special Angles sin30˚ = cos30˚ = tan30˚ = sin45˚ = cos45˚ = tan45˚ = 1 sin60˚ = cos60˚ = tan60˚ = HW#8) Find exact values of 6 trigs for: 3 6 Ch4.3A p338 1-22(a,b) Quiz tomorrow – would u like 2 c a sample? Θ

42. Trigonometry & Vector Components S O H C A H T O A in pp yp os dj yp an pp dj opp hyp sinΘ = adj hyp cosΘ = opp adj tanΘ =

43. Ch4.3A p338 1-22(a,b)

44. Ch4.2 Quiz Name___________ • Find exact values:˚ • A B C D • 1. sin 30˚ 1. cos 30˚ 1. sin 60˚ 1. cos 60˚ • 2. tan 30˚ 2. tan 60˚ 2. sin 30˚ 2. cos 30˚ • 3. cos 60˚ 3. sin 60˚ 3. tan 45˚ 3. tan 30˚ • 4. tan 45˚ 4. cos 45˚ 4. cos 60˚ 4. sin 60˚ • 5. sin 60˚ 5. cos 60˚ 5. tan 30˚ 5. tan 45˚ • 6. cos 45˚ 6. tan 45˚ 6. cos 45˚ 6. sin 45˚

45. Ch4.3B – Trig Identities Reciprocals: sin θ = cosθ = tan θ = cscθ = sec θ = cot θ = Combos: Pythag: Quiz in 2 days on these identities.

46. Ex4) Let θ be acute angle, with sin θ = 0.6, find: a) cos θ b) tan θ Ex5) Let θ be acute, with tan θ = 3, find: a) cot θ b) sec θ θ˚ θ˚

47. Ex6) Use a calc to eval: a) cos28˚ b) sec 28˚ c) sec 5˚40’ Ex7) Find the value of θ in radians and degrees: a) sin θ = b) cosθ = b) cscθ = 2 Ex8) Use calc to find θ in: a) degrees for cos θ = 0.3746 b) radians for sin θ = 0.3746 Ch4.3B p339 23-31odd,37-40all(a only),47-55all(a only) Quiz in 2 days

48. Ch4.3B p339 23-31odd,37-40all(a only), 47-55all(a only)

49. Ch4.3B p339 23-31odd,37-40all(a only), 47-55all(a only)

50. Ch4.3B p339 23-31odd,37-40all(a only), 47-55all(a only)