Pick a branch of sin⁻¹
"Pick a branch of sin⁻¹" is a free, interactive Class 12 Maths simulation for JEE, built on the lesson "sin⁻¹ and its principal branch" in Inverse Trigonometric Functions. The grey wave is y = sin x reflected in y = x, so every point on it has sin y = x. The dashed line through your x meets the wave several times: many angles share one sine. The thick arc is the branch you have chosen, and it meets the line exactly once. Sin⁻¹ needs a branch because many angles share a sine. The principal branch [−π/2, π/2] is the default: sin⁻¹ x always means the one angle there whose sine is x. JEE Main asked 25 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson sin⁻¹ and its principal branch in Inverse Trigonometric Functions. Change the values and watch what happens.
In JEE Main
42 shifts analysed
25 questions from Inverse Trigonometric Functions across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §2.2
- Restricted to [−π/2, π/2], sine is one-one and onto [−1, 1]. Its inverse is sin⁻¹ : [−1, 1] → [−π/2, π/2], also written arc sin.
- y = sin⁻¹ x means: y is the angle in [−π/2, π/2] whose sine is x. So sin⁻¹(1/2) = π/6 and not 5π/6, even though sin 5π/6 = 1/2 too, because 5π/6 lies outside [−π/2, π/2].
- sin⁻¹ is an increasing function. It runs from sin⁻¹(−1) = −π/2 through sin⁻¹ 0 = 0 to sin⁻¹ 1 = π/2.
- It is odd: sin⁻¹(−x) = −sin⁻¹ x, because the principal interval is symmetric about 0. So sin⁻¹(−1/2) = −π/6.
- sin⁻¹ x is undefined for |x| > 1: no angle has a sine of 2.
- On another branch the answers shift. On the branch with range [π/2, 3π/2], the angle whose sine is 1/2 is 5π/6; on [−3π/2, −π/2] it is −7π/6. These are not principal values.
- The −1 is part of the name, not a power: sin⁻¹ x is an angle, while (sin x)⁻¹ = 1/sin x = cosec x. The same holds for every trigonometric function.
Questions
3 answers
- What does the "Pick a branch of sin⁻¹" simulation show?
- The grey wave is y = sin x reflected in y = x, so every point on it has sin y = x. The dashed line through your x meets the wave several times: many angles share one sine. The thick arc is the branch you have chosen, and it meets the line exactly once.
- Does JEE Main ask questions from Inverse Trigonometric Functions?
- Yes. JEE Main asked 25 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 "sin⁻¹ and its principal branch" in Inverse Trigonometric Functions (Class 12 Maths).
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