Mathematics Multiple Choice Questions on “Trigonometric Functions – Angles”.
1. If the initial side is overlapping on the terminal side, then angle is ________
a) 0°
b) 180°
c) 90°
d) 270°
Answer: a
Clarification: The angle is formed if we start to rotate from initial side till terminal side comes. If they both overlap then angle is said to be 0°.
2. If we start to rotate and after completing one revolution again initial side overlap with terminal side, then the angle formed is _________
a) 0°
b) 180°
c) 90°
d) 360°
Answer: d
Clarification: The angle is formed if we start to rotate from initial side till terminal side comes. If we start to rotate and after completing one revolution again initial side overlap with terminal side, then the angle formed is 360°.
3. 1 radian is _______________
a) 54°48’
b) 57°16’
c) 180°
d) 17°46’
Answer: b
Clarification: We know, π radian = 180 degree
1 radian = 180/π degree = 57.27° = 57° (0.27*60)’ = 57°16’.
4. 1 degree is _________ radian.
a) π
b) 0.046
c) 0.1746
d) 0.01746
Answer: d
Clarification: 180 degree = π radian
1 degree = π/180 radian = 0.01746 radian.
5. 4 radians = _____________
a) 720°
b) 240°51’53”
c) 229°10’59”
d) 233°11’48”
Answer: c
Clarification: We know, π radians = 180 degrees
1 radian = 180/π degrees
4 radians = 720/π degrees = 229.183° = 229° (0.183*60)’ = 229 (10.98)’ = 229°10’59”.
6. If angle of arc is 60° and the length of arc is 20 cm. Find the radius of the circle from which arc is intercepted.
a) 18.08 cm
b) 17.07 cm
c) 19.09 cm
d) 18 cm
Answer: c
Clarification: 180 degree = π radian
1 degree = π/180 radians
60 degrees = 60* π/180 radians = π/3 radians
Angle=Arc length/Radius
π/3 = 20/Radius => Radius = 60/π = 19.09 cm.
7. If length of arc is 40 cm and radius of circle of arc is 10 cm then find the angle made by the arc.
a) 720°
b) 240°51’53”
c) 229°10’59”
d) 233°11’48”
Answer: c
Clarification: We know, Angle=Arc length/Radius
Angle = 40/10 = 4 radians
π radians = 180 degrees
1 radian = 180/π degrees
4 radians = 720/π degrees = 229.183° = 229° (0.183*60)’ = 229°(10.98)’= 229°10’59”.
8. The second hand of the watch is 2 cm long. How far the tip will move in 40 seconds?
a) 6.28 cm
b) 12.56 cm
c) 3.14 cm
d) 1.57 cm
Answer: b
Clarification: Radius of circle=2 cm
In 60 seconds, angle covered by second hand is 360°
In 40 seconds, angle covered by second hand is 360°*4/6 = 240°
240°=240*
Angle=Arc length/Radius
240*π/180 = Arc length/2
Arc length=8 π/3 = 12.56 cm.
9. If in two circles, arcs of the same length subtend angles 45° and 60° at Centre, find the ratio of their radii.
a) 2:3
b) 2:5
c) 3:4
d) 4:3
Answer: d
Clarification: Given θ1=45° and θ2=60°, L1=L2
We know, θ = l/r
r1 θ1 = r2 θ2
r1/r2=60/45=4/3.
So, radii are in ratio 4:3.
10. If minute hand covers 24 cm length in 30 minutes, then how much length minute hand have?
a) 19.1 cm
b) 38.2 cm
c) 57.3 cm
d) 45 cm
Answer: b
Clarification: In 60 minutes, angle covered by minute hand is 360°.
In 30 minutes, angle covered by minute hand is 180°.
L=24 cm, θ=180°=π
θ=L/r => π=24/r => r=24/π = 38.2 cm.