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Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Commerce MCQ


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5 Questions MCQ Test - Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions for Commerce 2024 is part of Commerce preparation. The Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions questions and answers have been prepared according to the Commerce exam syllabus.The Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions below.
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Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 1
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): sin-1(sin(2π/3)) = 2π/3

Reason (R): sin -1(sin θ) = θ, if q ∈ [(-π)/2, π/2]

Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 1
The principal value branch of sin–1x is [(-π)/2, π/2]

Let x = sin θ ⇒ θ = sin–1x

sin–1(sin θ) = sin–1 x = θ

sin–1(sin θ) = θ, if θ ∈ [(-π)/2, π/2]

Hence R is true.

Hence A is false.

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 2
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Principal value of cos–1(1) is π

Reason (R): Value of cos 0° is 1

Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 2
In case of Assertion

cos-1(1) = y

Cos y= 1

Cos y = cos 00 [∴ cos 00 = 1]

∴ y = 0

⇒ Principal value of cos–1 (1) is 0

Hence Assertion is in correct.

Reason is correct.

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Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 3
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Range of tan–1x is [(-π/2, π/2)]

Reason (R): Domain of tan–1x is R.

Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 3

Domain of tan x is the set {x : x ∈ R and x ≠ (2n + 1) π/2, n ∈ Z} and Range is R.

⇒ tan x is not defined for odd multiples of π/2.

If we restrict the domain of tangent function to [(-π)/2, π/2], then it is one-one and onto with its range as R. Actually tan x restricted to any of the intervals etc., is bijective and its range is R.

Thus tan–1x can be defined as a function whose domain is R and range could be any of the intervals and soon.

∴ Both A and R are true but R is not correct explanation of A.

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 4
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): Range of cot–1 x is (0, π)
Reason (R): Domain of tan–1 x is R.
Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 4

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 5
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Principal value of sin-1(1/√2) is π/4

Reason (R): Principal value of cot-1(-1/√3) is π/3
Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 5
sin-1(1/√2) = sin-1(sin (π/4))

= π/4

cot-1((-1/√3) = y

Cot y = -1/√3

= -cot(π/3)

= -cot (π - (π/3)

= cot(2π/3)

⇒ cot-1(-1/√3) = 2π/3

Hence Assertion is correct and Reason is incorrect.

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