3.01 - Arc Length and Radians - Edubirdie

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High School
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High School Physics
Academic year:

2024
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11
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Trigonometry Lesson 3.01 – Arc Length and Radians Arc Length (𝑙) O The distance of the edge of a circle that is cut during a rotation around the circumference. O Proportional to the angle n 𝑛 𝑙 = 360 2𝜋𝑟 Ex 1: Arc Length (𝑙) 𝑟 = 3𝑐𝑚 𝑛 = 170° 170 𝑙 = 360 2𝜋(3) 17 𝑙 = 36 6𝜋 17𝜋 𝑙= 6 𝑙 ≈ 8.9cm 𝑙 Radian O Abbreviated: rad O Like the degree, a radian is an angle measurement O In a circle, one radian is the measure of the central angle when the arc length is equal to the radius. O 𝑙=𝑟 𝑛 𝑙 = 360 2𝜋𝑟 Radian O 𝑙=𝑟 𝑛 𝑙 = 360 2𝜋𝑟 𝑛 𝑟 = 360 2𝜋𝑟 360 180 𝑛= = 2𝜋 𝜋 𝑛 = 57.29577951° Visually 𝜃 𝜃 = 57.29577951° = 1 rad A FULL CIRCLE 360° = 2𝜋 rad so 180° = 𝜋 rad Finding arc length from degrees or radians 𝑛 𝑙 = 360 2𝜋𝑟 𝑙 𝜃 = 2𝜋𝑟 2𝜋 𝑛𝜋 𝑙=𝑟 180 𝑙 = 𝑟𝜃 If given Degrees If given Radians Angle Conversion 𝜋 𝜃 = 𝑛( ) 180 180 𝑛 = 𝜃( ) 𝜋 Degrees to radians Radians to degrees Ex 2: Angle Conversion O Convert 225° to radians (exact expression) 𝜋 𝜃 = 225( ) 180 5𝜋 𝜃= 4 O Convert 11π/6 to degrees 11𝜋 180 ( ) 6 𝜋 𝑛 = 330° 𝑛= Homework O VISIONS 2 (blue book!) O p91: 1aceg, 2aceg, 3aceg O Worksheet – Arc Length – Trig Ratios (Q1-8)

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