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2.1 Degrees and Radians

2.1 Degrees and Radians. Degree and radian measure of angles Angles in standard position Arc length and area of a sector of a circle. Radian Measure of Central Angles. Example: Find the radian measure of the central angle subtended by an arc of 32 cm in a circle of radius 8 cm.

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2.1 Degrees and Radians

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  1. 2.1 Degrees and Radians • Degree and radian measure of angles • Angles in standard position • Arc length and area of a sector of a circle

  2. Radian Measure of Central Angles • Example: • Find the radian measure of the central angle subtended by an arc of 32 cm in a circle of radius 8 cm. • Solution: q = 32cm/8cm = 4 rad

  3. Radian-Degree Conversion Formulas • Example: • Find the radian measure of -1.5 rad in terms of p and in decimal form to 4 decimal places. • Solution: qd = (qr)(180º/p rad) = • (-1.5)(180/p) = 270º/p = -85.9437º

  4. Angles in Standard Position

  5. Sketching angles in Standard Position • Sketch these angles in standard position: A. -60º B. 3p/2 rad C. -3p rad D. 405º

  6. Coterminal Angles • Angles that differ by an integer multiple of 2 p or 360º are coterminal. • Example: Are the angles –p/3 rad and 2p/3 rad coterminal? Solution: (-p/3) – (2p/3) = -3p/3 = -pNo • Example: Are the angles -135º and 225º coterminal? Solution: -135º - (-225º) = -1(360)º Yes

  7. Area of a Sector of a Circle • A = ½ r2q, r = radius and q = central angle • Example: In a circle of radius 3 m find the area of the sector with central angle 0.4732. Solution: A = ½ 3m2(0.4732) ≈ 2.13 m2

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