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4.1 Radian and Degree Measure

4.1 Radian and Degree Measure. Terminal side. Initial side. Coterminal Angles. Angles that differ by multiples of 360 degrees or 2 radians. Find a positive and negative coterminal angle for each of the following. a. b. What is a radian?. 3 radians. 2 radians. 1 radian. r=1.

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4.1 Radian and Degree Measure

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  1. 4.1 Radian and Degree Measure Terminal side Initial side

  2. Coterminal Angles Angles that differ by multiples of 360 degrees or 2 radians. Find a positive and negative coterminal angle for each of the following. a. b.

  3. What is a radian? 3 radians 2 radians 1 radian r=1

  4. Complementary Angles – two angles are complementary if their sum is 90 degrees or Supplementary Angles have a sum of 180 degrees or Find the complementary and supplementary angles for

  5. Conversions: Radians Degrees To convert degrees to radians, multiply by To convert radians to degrees, multiply by Converting an angle from to decimal form.

  6. Arc Length s s = arc length r = radius theta = radian measure r = 4 in. First, we need to convert degrees to radians.

  7. Area of a Sector of a Circle where is measured in radians A sprinkler on a golf course fairway is set to spray water over a distance of 70 feet and rotates through an angle of 120 degrees. Find the area of the fairway watered by the sprinkler. 120o = how many radians? 70 ft 79-99 odd, 107

  8. Linear and Angular Speeds Consider a particle moving at a constant speed along a circular arc of radius r. If s is the length of the arc traveled in time t, then the linear speed v of the particle is Linear speed v Moreover, if is the angle (in radian measure) corresponding to the arc length s, then the angular speed (the lowercase Greek letter omega) of the particle is Angular speed A relationship between linear speed and angular speed is

  9. Finding Linear Speed The second hand of a clock is 10.2 cm long. Find the linear speed of the Tip of the second hand as it passes around the clock face. Linear speed v Arc length s =1.068 cm/sec

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