Class 12 Inverse Trigonometric Functions Important Questions (With Answers)

IMPORTANT MCQ

This section covers MCQs from CBSE Class 12 Mathematics INVERSE TRIGONOMETRY

IMPORTANT 2 MARKS

This section covers 2mark questions from CBSE Class 12 Mathematics INVERSE TRIGONOMETRY

Q08. Find the codomain of f(x)=2x, A={1,2,3,4}

f(1)=2, f(2)=4, f(3)=6, f(4)=8
Answer: B = {2, 4, 6, 8}

Q09. Check whether f(x)= (x−2)/(x−3) is one–one and onto

Solve y = (x−2)/(x−3). We get x = (3y − 2)/(y − 1).
Every y ≠ 1 has a unique x and y = 1 is not possible.
Answer: f is bijective.

Q10. Evaluate sin⁻¹(sin 3π/4) + cos⁻¹(cos 3π/4) + tan⁻¹(1)

sin⁻¹(√2/2) = π/4
cos⁻¹(−√2/2) = 3π/4
tan⁻¹(1) = π/4
Answer: 5π/4

Q11. Evaluate sin⁻¹(sin 3π/4) + cos⁻¹(cos π) + tan⁻¹(1)

sin⁻¹(√2/2) = π/4
cos⁻¹(−1) = π
tan⁻¹(1) = π/4
Answer: 3π/2

Q12. Range of y = cos⁻¹(x) for x ∈ [−1, 0]

cos⁻¹(x) decreases from π to π/2 as x goes −1 to 0.
Range: [π/2, π]

Q13. Evaluate 3 sin⁻¹(1/√2) + 2 cos⁻¹(√3/2) + cos⁻¹(0)

3 × (π/4) = 3π/4
2 × (π/6) = π/3
cos⁻¹(0) = π/2
Answer: 19π/12

Q14. Domain of y = sin⁻¹(x² − 4)

−1 ≤ x² − 4 ≤ 1 ⇒ 3 ≤ x² ≤ 5
Domain: [−√5, −√3] ∪ [√3, √5]

Q15. Find cos⁻¹(cos(−7π/3))

cos(−7π/3) = cos(π/3) = 1/2
cos⁻¹(1/2) = π/3
Answer: π/3

Q16. Domain and Range of f(x) = tan⁻¹(x)

Domain: ℝ
Range: (−π/2, π/2)

Q17. Range of sin⁻¹(x) for x ∈ [−1/√2, 1/√2]

sin⁻¹(−1/√2) = −π/4
sin⁻¹(1/√2) = π/4
Range: [−π/4, π/4]

3Mark Questions