Class XI Chapter 3 – Trigonometric Functions Maths ______________________________________________________________________________ Question 3: A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second? Solution 3: Number of revolutions made by the wheel in 1 minute = 360 Number of revolutions made by the wheel in 1 second 360 6 60 In one complete revolution, the wheel turns an angle of 2 radian. Hence, in 6 complete revolutions, it will turn an angle of 6 2 radian, i.e., 12 radian Thus, in one second, the wheel turns an angle of 12 radian. Question 4: Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm. 22 Use 7 Solution 4: We know that in a circle of radius r unit, if an arc of length at the centre, then 1 r Therefore, for r 100 cm, l 22 cm, we have 22 180 22 180722 radian degree degree 100 100 22100 126 3 degree 12 degree 1236' 1 60' 10 5 Thus, the required angle is 12 36' . l unit subtends an angle radian Question 5: In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord. Solution 5: Diameter of the circle = 40 cm Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 3 – Trigonometric Functions Maths ______________________________________________________________________________ r Radius of the circle length 20 cm 40 cm 20cm 2 Let AB be a chord of the circle. In OAB, OA OB Radiusof circle 20cm Also, AB = 20 cm Thus, is an equilateral triangle. OAB 60 radian 3 We know that in a circle of radius r unit, if an arc of length l the centre then l r AB̂ 3 ⇒ AB̂ = 20π 20 3 cm Thus, the length of the minor arc of the chord is 20 3 cm . unit subtends an angle radian at Question 6: If in two circles, arcs of the same length subtend angles 60 and 75 at the centre, find the ratio of their radii. Solution 6: Let the radii of the two circles be and r 2 . Let an arc of length l subtend an angle of 60 at the centre of the circle of radius r 1 , while let an arc of length/subtend an angle of 75 at the centre of the circle of radius r 2 . Now, 5 60 radian and 75 radian 3 12 We know that in a circle of radius r unit, if an arc of length at the centre then l or l r r r 1 l unit subtends an angle . radian Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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