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4.1 Angle Measure

4.1 Angle Measure. y. x. Standard Position : an angle drawn in the xy-plane w/ the vertex at the origin and the initial side on the positive x-axis. Counterclockwise = Positive Angle Clockwise = Negative Angle. To convert… degrees to radians, multiply by:

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4.1 Angle Measure

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  1. 4.1 Angle Measure

  2. y x Standard Position: an angle drawn in the xy-plane w/ the vertex at the origin and the initial side on the positive x-axis.

  3. Counterclockwise= Positive Angle • Clockwise= Negative Angle

  4. To convert… • degrees to radians, multiply by: • radians to degrees, multiply by:

  5. Ex 1: Find the radian measure of the angle:

  6. Ex 2: Find the degree measure of the angle: a) b)

  7. Coterminal Angles: 2 angles who have the same terminal sides. • To find positive or negative coterminal angles: Add or Subtract 360 or 2.

  8. Ex 3: Find 1 positive & 1 negative angle that are coterminal with the angle: a) b)

  9. Ex 4: Are the angles coterminal?

  10. Length of a Circular Arc: • s = arc length • r = radius •  = angle measure (rad)

  11. Area of a Circular Sector: • A = sector area • r = radius •  = angle measure (rad)

  12. Ex 5: Find the length of an arc that subtends a central angle of 45 in a circle of radius 10 m.

  13. Ex 6: A sector of a circle of radius 24 mi has an area of 288 mi2. Find the central angle of the sector.

  14. B 1 C A 1 • Radian: If a circle of radius 1 is drawn w/ the vertex of an angle at its center, then the measure of the angle in Radians (rad) is the length of the arc that subtends the angle. mBAC = length of Arc BC Circumference = 2

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