Test: Measurement of Angles - JEE MCQ

= 6.280 cm

As the angle increases from 270° to 360°, the sine increases from -1 to 0. As the angle increases from 270° to 360°, and the value of cos 270° = 0
and cos 360° = 1
So, the cosine increases from 0 to +1.

Length of arc = 15 cm
Radius: R = 6 cm
Arc length = R*θ
(θ is the angle subtended by the arc)
15 = 6*θ
θ = 5/2 radians

In The Third Quadrant
As the angle increases from 180° to 270°, the sine increases in magnitude but is now negative, so, the sine decreases from 0 to -1.

Second quadrant is from 90° to 180°
As we know that cos90° = 0, cos180° = -1
So the value of cos is decreasing from 0 to -1

First of all change the speed into m/s. You will get 4 m/s. It means that the wheel moves 4 metres a second i.e arc subtended by the wheel per second is 4m. Now, as we know that angle= arc÷radius. So, divide 4m by 0.35m ( convert 35 cm into metre or 4m into cm, as you wish). So, angle= (400÷35) radians = 80/7 radians. So, the answer is b).

The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.

1^ο= π\180
so 135^ο 
135×π\180
=3π\4

length of arc = 350m
Speed = 7km/hr
In one minute = (7*5/18*60)
=> (35*20)/6
= length of arc/radius
θ = (35*20)/(6*350)
θ = 1/3 radian

 r =7 m, θ = 1°
Length subtended by Arc = (2πr/360o)×θ
= (2×22×7×1)/(7×360)
​= 0.12m

We know angle described by minute hand in 60 mins = 360°
Angle described by the minute hand in one minute = 360°/60 = 6°
Time interval between 9AM to 9:35 AM = 35 min

Number of revolutions made by the wheel in 1 minute = 360
∴ Number of revolutions made by the wheel in 1 second = 360/(60) = 6
In 3 seconds = (6*3) = 18
In one complete revolution, the wheel turns an angle of 2π radian.
Hence, in 6 complete revolutions, it will turn an angle of 18 × 2π radian, i.e.,
36 π radian
Thus, in one second, the wheel turns an angle of 36π radian.

Radius of circle =14cm
An angle = 135^o
Length of arc = ?
We know that, Length of arc = Radius × Angle
= 14 * 3π/4
= 14 * (3*22)/(7*4)
= 33cm

We know that in a circle of radius r units, if an arc of length l units subtends an angle theta radian at the centre, then θ = l/ r.
Here, r = 7 m (length of rope will be equal to radius) and l = 210 m (length of arc will be the length which the cow grazed)
Thus, θ = 210^o/ 7 
= 30^o