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1.1 Arc Length

1.1 Arc Length. s = r . r. C = 2 r. What does r stand for?. What does 2  stand for?. This information can help us develop a new formula…. This is called the Arc Length Formula. What does r stand for?. s. r. . What does  stand for?. s = r . What does s stand for?.

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1.1 Arc Length

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  1. 1.1 Arc Length s = r

  2. r C = 2r What does r stand for? What does 2 stand for? This information can help us develop a new formula…

  3. This is called the Arc Length Formula. What does r stand for? s r  What does  stand for? s = r What does s stand for? Units of measure must match. Must be measured in radians.

  4. How to use the Arc Length Formula. Example #1: Given:r = 32 cm and  = 3 radians. Find:s (the arc intercepted by a 32 cm radius rotated through 3 radians). s = r  Units must match. s = 32 (3) s = 96 cm

  5. How to use the Arc Length Formula. Example #2: Given:r = 6 in. and  = 30 Find:s (the arc intercepted by a 6 in. radius rotated through 30). Can’t use…must be a radian. s = r  s = 6 (30) s = 6 (/6) Units must match. s = in.

  6. How to use the Arc Length Formula. Example #3: Given:r = 15 in. and s = 35 in. Find: (the angle through which a radius of 15 in. was rotated to intercept an arc that measures 35 in.). s = r  The angles are measured in radians. 35 = 15 ()  = 35/15  = 7/3 radians

  7. How to use the Arc Length Formula. Example #4: Given:r = 6 in. and s = 2 ft. Find: (the angle through which a radius of 6 in. was rotated to intercept an arc that measures 2 ft). The units of measure must match. s = r  The angles are measured in radians. 2 = 6() 24= 6() = 4 radians

  8. How to use the Arc Length Formula. Example #5: Given:s = 20 mi. and  = /2 Find:r (the radius that was rotated /2 radians and intercept an arc that measured 20 mi.). The units of measure must match. s = r  20 = r(/2) 40/ = r r = 40/miles

  9. How to use the Arc Length Formula. Example #6: Given:s = 36 yd. and  = 60 Find:r (the radius that was rotated 60 and intercept an arc that measured 36 yd.). Can’t use…must be a radian. The units of measure must match. s = r  36 = r(60) 36 = r(/3) 108/ = r r = 108/yd

  10. More Arc Length Formula Applications: • Draw Pictures • Apply s = r  for every pie shaped figure in the picture. Let’s try…

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