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Ch4.1A – Radian and Degree Measure r . 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

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

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**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**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**Ex1) Find the acute angle equivalent to**Ex2) Find the negative angle equivalent to Ex3) Find the positive angle equivalent to**Ex4) Find the complement and supplement**angles to a) b)**Degree/Radian Conversions**Conversions: Conversion Factor:**Ex5) Convert:**a) 135˚ b) -270˚ c) d) 2 rad (Quiz on conv in 2 days) Ch4.1A p318 5-19odd,45-55odd**Ch4.1A p318 5-19odd,45-55odd**Quiz tomorrow! (On conversions)**Ch4.1B – Arc Length**(Quiz tomorrow!) r**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˚.**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.**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?**Ch4.1B p319 35-41odd,**52,54,71-81odd,91,95 (Do #35 and #39 in class) (Quiz tomorrow on conversions!)**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˚**Ch4.2 – The Unit Circle**x2 + y2 = 1 Ex1) 45˚ = _____ rad x = _____ y = _____**Ex2) 60˚ = _____ rad**x = _____ y = _____ Ex3) 30˚ = _____ rad x = _____ y = _____ Ex5) 90˚ = _____ rad Ex4) 0˚ = _____ rad x = _____ x = _____ y = _____ y = _____**Ex6)**x = _____ x = _____ y = _____ y = _____ x = _____ x = _____ y = _____ y = _____**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)**Ch4.2B – Trig Functions**sin t = y (cosecant) csct = cost = x (secant) sec t = tan t = (cotangent) cot t = Ex8) Eval 6 trigs for:**sin t= ycsct =**cost = x sec t = tan t = cot t = Ex9) Eval: a) b)**x = costy = sin t**Domains: (what you put in for t) Ranges: (what you get out for x or y)**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)**Ch4.3 – Right Triangle Trig**SOH-CAH-TOA sin θ = cosθ = tan θ = hypotenuse opposite Θ adjacent**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**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˚**Ex3) Use the equilateral triangle to find the value of**sin60˚, cos60˚, sin30˚, cos30˚**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**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**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 =**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˚**Ch4.3B – Trig Identities**Reciprocals: sin θ = cosθ = tan θ = cscθ = sec θ = cot θ = Combos: Pythag: Quiz in 2 days on these identities.**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˚**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

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