Find the best tutors and institutes for Class 11 Tuition
Search in
Find the radian measures corresponding to the following degree measures:
(i) 25° (ii) – 47° 30' (iii) 240° (iv) 520°
(i) 25°
We know that 180° = π radian
(ii) –47° 30'
–47° 30' =
degree [1° = 60']
degree
Since 180° = π radian
(iii) 240°
We know that 180° = π radian
(iv) 520°
We know that 180° = π radian
Find the degree measures corresponding to the following radian measures
.
(i) 
(ii) – 4 (iii) 
(iv) 
(i)
We know that π radian = 180°
(ii) – 4
We know that π radian = 180°
(iii)
We know that π radian = 180°
(iv)
We know that π radian = 180°
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Number of revolutions made by the wheel in 1 minute = 360
∴Number of revolutions made by the wheel in 1 second =
In one complete revolution, the wheel turns an angle of 2π radian.
Hence, in 6 complete revolutions, it will turn an angle of 6 × 2π radian, i.e.,
12 π radian
Thus, in one second, the wheel turns an angle of 12π radian.
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
.
We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then
Therefore, forr = 100 cm, l = 22 cm, we have
Thus, the required angle is 12°36′.
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
Diameter of the circle = 40 cm
∴Radius (r) of the circle =
Let AB be a chord (length = 20 cm) of the circle.
In ΔOAB, OA = OB = Radius of circle = 20 cm
Also, AB = 20 cm
Thus, ΔOAB is an equilateral triangle.
∴θ = 60° =
We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then
.
Thus, the length of the minor arc of the chord is
.
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Let the radii of the two circles be
and
. Let an arc of length l subtend an angle of 60° at the centre of the circle of radius r1, while let an arc of length l subtend an angle of 75° at the centre of the circle of radius r2.
Now, 60° =
and 75° =
We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then
.
Thus, the ratio of the radii is 5:4.
Find the angle in radian though which a pendulum swings if its length is 75 cm and the tip describes an arc of length
(i) 10 cm (ii) 15 cm (iii) 21 cm
We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then
.
It is given that r = 75 cm
(i) Here, l = 10 cm
(ii) Here, l = 15 cm
(iii) Here, l = 21 cm
How helpful was it?
How can we Improve it?
Please tell us how it changed your life *
Please enter your feedback
UrbanPro.com helps you to connect with the best Class 11 Tuition in India. Post Your Requirement today and get connected.
Find best tutors for Class 11 Tuition Classes by posting a requirement.
Get started now, by booking a Free Demo Class
