Inverse Trigonometric Functions Practice Questions

Class 12 · Mathematics · 1949 free MCQs with instant results and detailed explanations.

1949

Total

699

Easy

875

Medium

375

Hard

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Topics in Inverse Trigonometric Functions

Principal Value 712

Properties 661

Simplification 576

Sample Questions from Inverse Trigonometric Functions

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

What is the value of sin^(-1)(1)?

A. π/2

B. 0

C. π

D. 1

Show Answer & Explanation

Correct Answer: A

The value of sin^(-1)(1) is π/2 because sine of π/2 is 1.

Easy

What is the range of the function tan^(-1)(x)?

A. (-π/2, π/2)

B. (0, π)

C. (−1, 1)

D. (−π, π)

Show Answer & Explanation

Correct Answer: A

The range of tan^(-1)(x) is (-π/2, π/2).

Easy

What is the derivative of sin^(-1)(x)?

A. 1/√(1-x^2)

B. 1/x

C. √(1-x^2)

D. x/√(1+x^2)

Show Answer & Explanation

Correct Answer: A

The derivative of sin^(-1)(x) is 1/√(1-x^2).

Medium

If sin⁻¹(x) + cos⁻¹(x) = π/2, what is the value of x?

A. 0

B. 1

C. √2

D. 1/2

Show Answer & Explanation

Correct Answer: B

The identity states that the sum of arcsine and arccosine of the same value equals π/2 when the input is valid, which occurs at x=1.

Medium

What is the derivative of y = sin⁻¹(x) with respect to x?

A. 1/√(1-x²)

B. 1/√(1+x²)

C. √(1-x²)

D. 1/x

Show Answer & Explanation

Correct Answer: A

The derivative of the arcsine function is given by 1/√(1-x²), valid for |x| < 1.

Medium

If x = sin⁻¹(1/2), what is cos(x)?

A. √3/2

B. 1/2

C. 1

D. √2/2

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Correct Answer: A

If x = sin⁻¹(1/2), then x = π/6, therefore cos(x) = cos(π/6) = √3/2.

Medium

Which of the following equations is true for all x in the domain of arcsin?

A. sin(arcsin(x)) = x

B. arcsin(sin(x)) = x

C. arccos(cos(x)) = x

D. tan(arcsin(x)) = x

Show Answer & Explanation

Correct Answer: A

The relationship sin(arcsin(x)) = x holds true for x in [-1, 1], which is the domain of arcsin.

Hard

If sin^(-1)(x) + cos^(-1)(x) = k, then what is the value of k?

A. π/2

B. π

C. 1

D. 0

Show Answer & Explanation

Correct Answer: A

The sum of the inverse sine and inverse cosine of the same value x equals π/2 for all x in the interval [-1, 1].

Hard

Evaluate the expression tan^(-1)(1) + tan^(-1)(1). What is the result?

A. π/2

B. π

C. 1

D. 0

Show Answer & Explanation

Correct Answer: A

Since tan^(-1)(1) = π/4, summing them gives π/4 + π/4 = π/2.

Q10

Hard

If tan^(-1)(x) = α, what is the equivalent expression for x in terms of α?

A. tan(α)

B. sin(α)

C. cos(α)

D. sec(α)

Show Answer & Explanation

Correct Answer: A

The definition of the inverse tangent function states that x = tan(α).

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Inverse Trigonometric Functions — Class 12 Mathematics Practice Questions Online

This page contains 1949 practice MCQs for the chapter Inverse Trigonometric Functions in Class 12 Mathematics. The questions are organized by difficulty — 699 easy, 875 medium, 375 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.