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What is a radian and why do we use them?*

What is a radian and why do we use them?*. * (Why not just use degrees?). What is a radian?. A radian is an angle measurement that gives the ratio:. When the length of the arc.  = 1 radian. equals the length of the radius. The angle has a measure of 1 radian. What is a radian?.

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What is a radian and why do we use them?*

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  1. What is a radian and why do we use them?* * (Why not just use degrees?)

  2. What is a radian? A radian is an angle measurement that gives the ratio: When the length of the arc  = 1 radian equals the length of the radius The angle has a measure of 1 radian

  3. What is a radian? A radian is an angle measurement that gives the ratio: When the length of the arc is twice as long as  = 2 radians the length of the radius The angle has a measure of 2 radians

  4. What is a radian? A radian is an angle measurement that gives the ratio: When the length of the arc is three times as long as  = 3 radians the length of the radius The angle has a measure of 3 radians

  5. What is a radian? A radian is an angle measurement that gives the ratio: When the length of the arc is πtimes aslong as  = π radians the length of the radius The angle has a measure of π radians

  6. What is a radian? A radian is an angle measurement that gives the ratio: A “unit circle” is a circle with radius = 1 and center at the origin.  (0,0) (1,0) radius=1 The radian measure of an angle for a unit circle is equal to the length of the arc that it subtends.

  7. Why do we use radians? Using radians make some formulas simple while the same formula is more complicated with degrees: Using degrees Angle measurement, , is Using radiansAngle measurement, , is where s is the arc length and r is the radius

  8. Why do we use radians? Radians are very important in Calculus. The area between y = sin (x) and the x-axis from 0 < x < 180is approximately 114.6 when graphed in degrees.

  9. Why do we use radians? Radians are very important in Calculus. The area between y = sin (x) and the x-axis from 0 < x < πis exactly 2 when graphed in radians.

  10. First usages of radians and degrees Muir, a mathematician, and James T. Thomson, a physicist, were working independently during the late nineteenth century to develop a new unit of angle measurement. They met and agreed on the name radian, a shortened form of the phrase radial angle. Different names were used for the new unit until about 1900. Today the term radian is in common usage." Source: Algebra 2, Bettye C. Hall and Mona Fabricant"James,1991 Prentice-Hall "The yonge sonne That in the Ram is foure degrees vp ronne" (OED2). He again used the word in about 1391 in A Treatise on the Astrolabe: "9. Next this folewith the cercle of the daies, that ben figured in manere of degres, that contenen in nombre 365, dividid also with longe strikes fro 5 to 5, and the nombre in augrym writen under that cercle." Source: Chaucer's Canterbury Tales, 1386

  11. What is a radian and why do we use them?* * (Why not just use degrees?)

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