18 January 2022 Radians LO To convert between

18 January 2022 Radians LO: To convert between radians and degrees www. mathssupport. org

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

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. www. mathssupport. org r x r r

Radians If the arc is 2 r, the angle is 2 radians. r O q = 2 radian = 2 rad. www. mathssupport. org 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. www. mathssupport. org 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° r O q = 3. 1416 p radian r = 3. 1416 p rad. = 180° 57. 3° Hence, 1 radian = www. mathssupport. org 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° 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 = = www. mathssupport. org 2 p radian 2 p rad. = 360°

Radians Convert 20° to radians radian p = x x 20° degrees 180° 20° = = Using these equivalences p Write the proportion 180° x 20°p = 180° x p 9 = www. mathssupport. org Solve for x rad

Radians Convert 60. 3° to radians radian p = x x 60. 3° degrees 180° 60. 3° = = Using these equivalences p Write the proportion 180° x 60. 3° p = 180° x 67 p rad = 200 www. mathssupport. org Solve for x or 1. 05 rad

Radians radian p = degrees 180° = x x 180° = p 180° ⨯ p x = 108° www. mathssupport. org Using these equivalences Write the proportion Solve for x

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