Exercise 9.1 (Solutions)
Math notes Textbook of Algebra and Trigonmetry for Class XI
Question # 1
Express the following sexagesimal measures of angles in radians:
(i) 30 (ii) 45 (x) 10 15′ (xii) 75 6′ 30′′
Solutions
π π
(i) 30 = 30 × radian = radian
180 6
π π
(ii) 45 = 45 × radian = radian
180 4
π 1025π 41π
(x) 10 15′ = 10.25 = 10.25 × radian = radian= radian
180 18000 720
π
(xii) 75 6′ 30′′ = 75.1083 = 75.1083 × radian
180
π π
= 751083 × radian = 9013 × radian
1800000 21600
Remaining do your self
Question # 2
Convert the following radian measures of angles into the measures of sexagesimal
system:
π 13
(i) rad (xii) π rad
8 16
Solutions
π 180
(i) rad. = = 22.5 ∵ π rad = 180
8 8
13 13
(xii) π rad. = × 180 = 146.25 ∵ π rad = 180
16 16
Remaining do your self
Question # 3
What is the circular measure of the angle between the heads of the watch at 4’O
clock?
Solution
Since total angle in watch = 2π rad.
2π π
Angel made by hands in 1 hour = = rad.
12 6
, FSc-I / 9.1 - 2
π 2π
Thus angle made by hand in 4 hours = 4 × = rad.
6 3
Question # 4
Find θ , when:
(i) l = 1.5 cm , r = 2.5 cm (ii) l = 3.2 m , r = 2m
Solution
(i) l = 1.5 cm , r = 2.5 cm
l 1.5
Since θ = ⇒ θ= = 0.6 rad.
r 2.5
(ii) l = 3.2 m , r = 2m
l 3.2
Since θ = ⇒ θ= = 1.6 rad.
r 2
Question # 5
Find l, when:
(i) θ = π rad. r = 6 cm (ii) θ = 65 20′ , r = 18 mm
Solutions
(i) θ = π rad. r = 6 cm
Since l = r θ
⇒ l = 6π = 6(3.14159) = 18.85 cm.
π 3.14159
(ii) θ = 65 20′ = 65 .33 = 65.33 × = 65.33 × = 1.1403 rad. ,
180 180
r = 18 mm
Since l = r θ
⇒ l = 18 × 1.1403 = 20.5254 mm
Question # 6
1
(i) Find r , when; l = 5 cm , θ = radian
2
(ii) Find r , when; l = 56 cm , θ = 45
Solutions
1
(i) l = 5 cm , θ = rad
2
1
Since l = r θ ⇒ 5=r× ⇒ r = 5 × 2 = 10 cm
2
π π
(ii) l = 56 cm , θ = 45 = 45 × = rad
180 4
π 4 224
Since l = r θ ⇒ 56 = r × ⇒ r = 56 × = = 71.30 cm
4 π 3.14159
Math notes Textbook of Algebra and Trigonmetry for Class XI
Question # 1
Express the following sexagesimal measures of angles in radians:
(i) 30 (ii) 45 (x) 10 15′ (xii) 75 6′ 30′′
Solutions
π π
(i) 30 = 30 × radian = radian
180 6
π π
(ii) 45 = 45 × radian = radian
180 4
π 1025π 41π
(x) 10 15′ = 10.25 = 10.25 × radian = radian= radian
180 18000 720
π
(xii) 75 6′ 30′′ = 75.1083 = 75.1083 × radian
180
π π
= 751083 × radian = 9013 × radian
1800000 21600
Remaining do your self
Question # 2
Convert the following radian measures of angles into the measures of sexagesimal
system:
π 13
(i) rad (xii) π rad
8 16
Solutions
π 180
(i) rad. = = 22.5 ∵ π rad = 180
8 8
13 13
(xii) π rad. = × 180 = 146.25 ∵ π rad = 180
16 16
Remaining do your self
Question # 3
What is the circular measure of the angle between the heads of the watch at 4’O
clock?
Solution
Since total angle in watch = 2π rad.
2π π
Angel made by hands in 1 hour = = rad.
12 6
, FSc-I / 9.1 - 2
π 2π
Thus angle made by hand in 4 hours = 4 × = rad.
6 3
Question # 4
Find θ , when:
(i) l = 1.5 cm , r = 2.5 cm (ii) l = 3.2 m , r = 2m
Solution
(i) l = 1.5 cm , r = 2.5 cm
l 1.5
Since θ = ⇒ θ= = 0.6 rad.
r 2.5
(ii) l = 3.2 m , r = 2m
l 3.2
Since θ = ⇒ θ= = 1.6 rad.
r 2
Question # 5
Find l, when:
(i) θ = π rad. r = 6 cm (ii) θ = 65 20′ , r = 18 mm
Solutions
(i) θ = π rad. r = 6 cm
Since l = r θ
⇒ l = 6π = 6(3.14159) = 18.85 cm.
π 3.14159
(ii) θ = 65 20′ = 65 .33 = 65.33 × = 65.33 × = 1.1403 rad. ,
180 180
r = 18 mm
Since l = r θ
⇒ l = 18 × 1.1403 = 20.5254 mm
Question # 6
1
(i) Find r , when; l = 5 cm , θ = radian
2
(ii) Find r , when; l = 56 cm , θ = 45
Solutions
1
(i) l = 5 cm , θ = rad
2
1
Since l = r θ ⇒ 5=r× ⇒ r = 5 × 2 = 10 cm
2
π π
(ii) l = 56 cm , θ = 45 = 45 × = rad
180 4
π 4 224
Since l = r θ ⇒ 56 = r × ⇒ r = 56 × = = 71.30 cm
4 π 3.14159
