RADIANS Radians, like degrees, are a way of measuring angles.

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Presentation transcript:

RADIANS Radians, like degrees, are a way of measuring angles

 One radian is equal to the angle formed when the arc opposite the angle is equal to the radius of the circle. So in the diagram, the angle Ө is equal to one radian since the arc AB is the same length as the radius of the circle.

So Ө = 1 radian Arc length = radius

 Now, the circumference of the circle is 2 Л r, where r is the radius of the circle.  So the circumference of a circle is 2 Л times larger than its radius.  This means that in any circle, there are 2 Л radians.

 Therefore 360° = 2 Л radians.  Therefore 180° = Л radians.  So one radian = 180/ Л degrees  one degree = Л /180 radians.

 To convert a certain number of degrees in to radians, multiply the number of degrees by Л /180  To convert a certain number of radians into degrees, multiply the number of radians by 180/ Л

Arc Length  The length of an arc of a circle is equal to r Ө where Ө is the angle, in radians, subtended by the arc at the centre of the circle.  So in the next diagram, s = r Ө

s = r Ө

Area of Sector  The area of a sector of a circle is ½r 2 Ө where r is the radius and Ө is the angle in radians subtended by the arc at the centre of the circle.  So in the next diagram, the shaded area is equal to ½ r 2 Ө

area = ½r 2 Ө