Radians Radians are units for measuring angles They

Radians are units for measuring angles. They can be used instead of degrees. Why

Radians 1 radian is defined as the size of the central angle subtended by

Radians If the arc is 2 r, the angle is 2 radians. r O

Radians If the arc is 2 r, the angle is 2 radians. If the

Degrees into Radians Convert 120 o to radians. We know that We want to

Degrees into Radians Convert 225 o to radians. We know that We want to

Radians into Degrees We know that We want to find Writing in the form

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Radians

Radians are units for measuring angles. They can be used instead of degrees. Why use radians? One complete turn is 360 o but the number 360 is a somewhat arbitrary measure. The Babylonians believed that there were 360 days in a year and hence used 360 o to represent one revolution. Radians, however, are directly related to measurements within a circle.

Radians 1 radian is defined as the size of the central angle subtended by an arc which is the same length as the radius of the circle. O x = 1 radian = 1 rad. r x r r

Radians If the arc is 2 r, the angle is 2 radians. r O q = 2 radian = 2 rad. r q 2 r

Radians If the arc is 2 r, the angle is 2 radians. If the arc is 3 r, the angle is 3 radians. r O q = 3 radian = 3 rad. r q 3 r

Radians If the arc is 2 r, the angle is 2 radians. If the arc is 3 r, the angle is 3 radians. p r, the angle is 3. 1416 If the arc is 3. 1416 p rads. But, pr is half the circumference of the circle so the angle is 180 o r O q = 3. 1416 p radian r = 3. 1416 p rad. = 180 o 57. 3 o Hence, 1 radian = q 3. 1416 pr

Radians If the arc is 2 r, the angle is 2 radians. If the arc is 3 r, the angle is 3 radians. p r, the angle is If the arc is p rads. But, pr is half the circumference of the circle so the angle is 180 o One complete turn around the circle is subtended by an arc O q equal in length to the circumference r of the circle 2 p r q = = 2 p radian 2 p rad. = 360 o

Degrees into Radians Convert 120 o to radians. We know that We want to find Writing in the form of a proportion Solving for x Simplifying p rad. = 180 o x rad. = 120 o

Degrees into Radians Convert 225 o to radians. We know that We want to find Writing in the form of a proportion Solving for x Simplifying p rad. = 180 o x rad. = 225 o

Radians into Degrees We know that We want to find Writing in the form of a proportion Solving for x Simplifying p rad. = 180 o = xo