What one radian looks like
"What one radian looks like" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Radian measure and arc length" in Trigonometric Functions. Slide θ to open the angle at the centre, and r to change the circle. The orange arc is the part of the circle the angle cuts off. Each black tick on the arc marks one more radius-length of arc. Θ in radians = arc length ÷ radius, so l = rθ. A full turn fits 2π ≈ 6.28 radii round the circle: 2π radians = 360°, so π radians = 180°. JEE Main asked 41 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Radian measure and arc length in Trigonometric Functions. Change the values and watch what happens.
In JEE Main
42 shifts analysed
41 questions from Trigonometric Functions across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §3.2.2
- In a circle of radius 1 unit (a unit circle), the angle at the centre made by an arc 1 unit long measures 1 radian. The same holds in any circle: an arc as long as the radius makes 1 radian at the centre.
- The whole circumference of a unit circle is 2π, so one complete revolution is 2π radians, a half turn is π radians and a quarter turn is π/2 radians.
- An arc twice as long makes twice the angle at the centre, so the angle is proportional to the arc. An arc of length l in a circle of radius r therefore makes θ = l/r radians at the centre; equivalently l = rθ.
- l = rθ holds only with θ in radians. For example, with π = 22/7, an arc of a circle of radius 21 cm making 60° = π/3 at the centre has length 21 × π/3 = 7π = 22 cm.
- A radian is a ratio of two lengths, so it has no dimensions; the word radian is often left out, and an angle written without a degree sign is read in radians.
- Radians match the real numbers: lay a number line along the tangent at a point A of the unit circle with 0 at A, and wrap the positive half anticlockwise and the negative half clockwise round the circle. Each real number x then lands at the point reached by an angle of x radians.
Questions
3 answers
- What does the "What one radian looks like" simulation show?
- Slide θ to open the angle at the centre, and r to change the circle. The orange arc is the part of the circle the angle cuts off. Each black tick on the arc marks one more radius-length of arc.
- Does JEE Main ask questions from Trigonometric Functions?
- Yes. JEE Main asked 41 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Radian measure and arc length" in Trigonometric Functions (Class 11 Maths).
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