...can. CIRCLE GEOMETRY Angles standing on the same arc of a circle and in the same segment are equal. The angle subtended at the centre of a circle by an arc is twice the angle subtended at the circumference by the same arc. The angle in a semicircle is a right...

...360; Amplitude = a and period = b For y = a tan bx° 1 80° Amplitude cannot be measured and period = The angle subtended at the centre of a circle by an arc equal in length to the radius is 1 radian. л radians = 180 sin 0 0 30° n 6 1 45° n 4 1 60° n У /3 2 90 n 2 COS 0...

...radians. Fig 4.24 Let's define the radian, which is shown in Fig 4.24 above. One radian (1 rad) is the angle subtended at the centre of a circle by an arc, s, with a length equal to the radius of a circle, r. Fig 4.25 For any angle 9 that is subtended by...

...exercise). The perpendicular bisector of a chord of a circle goes through the centre of the circle. The angle subtended at the centre of a circle by an arc, is twice the angle subtended at the circumference by the same arc. All angles subtended at the circumference...

...2 cos x = 0 33 sin 2 x + 3 cos 2 x = 2 34 3 sin x + 3 = cos 2 x SUMMARY OF KEY POINTS 1 1 radian is the angle subtended at the centre of a circle by an arc with length that is equal to the radius of the circle. 2 The length of an arc of a circle, radius r,...

...+ a) 6.2 Revision 6.2.1 Radian measure and the circle QHBEED As noted in Section 5.2.2, a radian is the angle subtended at the centre of a circle by an arc with length equal to that of the radius. It follows that 180 9 radians — 9 degrees 7T The length...

...between them. Angles can be measured in degrees or radian (rad). Irad = 57° Figure 4.1 One radian is the angle subtended at the centre of a circle by an arc of length equal to the radius (see Figure 4.1). arc length angle in radian = — radius Since the total...

...rather than degrees. Radians are an alternative system of angular measure. One radian is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. An angle measured in radians is thus Figure A2 Measuring an angle with an outstretched...

...into 60 minutes (') and each minute into 60 seconds ("). But the radian is more fundamental, being the angle subtended at the centre of a circle by an arc of the circumference that is equal in length to its radius. So there are 2jt radians in a circle of...

...need to reproduce the calculus definition of a radian for AS-Level. Definition arc = r A radian is the angle subtended at the centre of a circle by an arc of length equal to the radius. Important results are: 2 TT radians = 360° T7 radians = 180° The circumference...