which a central angle of ° intercepts an arc of length . cm (use π ). MATHEMATICS Solution Here l = . cm and θ = ° = π π radian = Hence, by r = θ l , we have r = .
× . × × π = . cm Example The minute hand of a watch is . cm long.
How far does its tip move in minutes? (Use π = . ). Solution In minutes, the minute hand of a watch completes one revolution.
Therefore, in minutes, the minute hand turns through of a revolution. Therefore, θ = × ° or π radian. Hence, the required distance travelled is given by l = r θ = . × π cm = π cm = × .
cm = . cm. Example If the arcs of the same lengths in two circles subtend angles °and ° at the centre, find the ratio of their radii. Solution Let r and r be the radii of the two circles.
Given that θ = ° = π × = π radian and θ = ° = π × = π radian Let l be the length of each of the arc. Then l = r θ = r θ , which gives π × r = π × r , i.e., r = Hence r : r = : . EXERCISE . .
Find the radian measures corresponding to the following degree measures: (i) ° (ii) – ° ′ (iii) ° (iv) ° TRIGONOMETRIC FUNCTIONS . Find the degree measures corresponding to the following radian measures (Use π ). – (iii) π (iv) π . A wheel makes revolutions in one minute.
Through how many radians does it turn in one second? . Find the degree measure of the angle