Inverse Trigonometric Functions Prep
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Inverse Trigonometric Functions Prep
English 44 leveled MCQs Free
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5 marks Long answer
Solve for x: 2tan^{-1}(x)+sin^{-1}(2x/(1+x^2))=4√3.
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x = 3
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5 marks Long answer
If α=sin^{-1}(√2/2)+cos^{-1}(−1/2) and β=tan^{-1}(√3)−cot^{-1}(−1/√3) then find the value of α+β.
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α+β = π
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5 marks Long answer
Draw the graph of principal value branch of cos^{-1}(x).
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Graph of cos^{-1}(x) from [−1,1] to [0,π]
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5 marks Long answer
Draw the graph of cos^{-1}(x) where x∈[−1,0]. Also, write its range.
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Graph of cos^{-1}(x) from [−1,0] to [π/2,π]. Range: [π/2,π]
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5 marks Long answer
Draw the graph of sin^{-1}(x), x∈[−1/√2,1/√2]. Also, write its range.
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Graph of sin^{-1}(x) from [−1/√2,1/√2] to [−π/4,π/4]. Range: [−π/4,π/4]
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5 marks Long answer
If a function f: A→B defined as f(x)=y is one-one and onto then we can define a unique function g: B→A such that g(y)=x, where x∈A and y∈B. Function g is called the inverse of function f. The domain of sine function is R and function sin: R→[−1, 1] is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from the set A to [-1, 1] such that inverse of sine function exists, i.e, sin^{-1}(x) is defined from [-1, 1] to A. On the above information, answer for the following questions: (i) If A is the interval other than principal value branch, give an example of one such interval. (ii) If sin^{-1}(x) is defined from [-1,1] to its principal value branch, find the value of sin^{-1}(−1/2)−sin^{-1}(1). (iii) (a) Draw the graph of sin^{-1}(x) from [-1, 1] to its principal value branch. (OR) (b) Find the domain and range of 2sin^{-1}(1−x).
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Example of A: (−∞,−1) or (1,∞); sin^{-1}(−1/2)−sin^{-1}(1) = −π/6; Graph of sin^{-1}(x) from [-1, 1] to [−π/2,π/2]
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3 marks Medium answer
Find the domain of sin^{-1}(−x/2).
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Domain: [−2,2]
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3 marks Medium answer
Find the domain of sin^{-1}(√x−1).
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Domain: [1,2]
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3 marks Medium answer
Find the domain of sin^{-1}(x^2−3).
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Domain: [−√3,√3]
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3 marks Medium answer
Find the domain of the function cos^{-1}(x^2−4).
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Domain: [−2,2]
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3 marks Medium answer
Find the domain of the function sec^{-1}(2x+1).
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Domain: x ≤ −1/2 or x ≥ 1/2
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3 marks Medium answer
Find the domain of sin^{-1}(x^2−4) and find its range.
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Domain: [−2,2], Range: [−π/2,π/2]
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3 marks Medium answer
Find the domain of cos^{-1}(1−x^2). Also, find its range.
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Domain: [−1,1], Range: [0,π]
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3 marks Medium answer
Write the domain and range (principal value branch) of tan^{-1}(x).
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Domain: ℝ, Range: (−π/2,π/2)
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3 marks Medium answer
Simplify tan^{-1}(cos(x)−sin(x)).
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tan^{-1}(cos(x)−sin(x))
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3 marks Medium answer
Simplify sin^{-1}(√(1+x^2)).
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sin^{-1}(√(1+x^2))
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3 marks Medium answer
Find the principal value of tan^{-1}(1+cos^{-1}(−1/2))+sin^{-1}(−1/√2).
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Principal value: π/4
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3 marks Medium answer
Evaluate: tan^{-1}[2sin(2cos^{-1}(√3/2))].
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tan^{-1}(√3)
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3 marks Medium answer
Evaluate: sin^{-1}(sin(3π/5)).
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sin^{-1}(sin(3π/5)) = 3π/5
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3 marks Medium answer
Evaluate: cos^{-1}(cos(−7π/3)).
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cos^{-1}(cos(−7π/3)) = 7π/3
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3 marks Medium answer
Evaluate: sin^{-1}(sin(3π/4))+cos^{-1}(cos(3π/4))+tan^{-1}(1).
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Evaluate: 3π/4 + 3π/4 + π/4
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3 marks Medium answer
Evaluate: sin^{-1}(sin(13π/6))+cos^{-1}(cos(π/3))+tan^{-1}(√3).
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Evaluate: 13π/6 + π/3 + π/3
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3 marks Medium answer
Evaluate: 3sin^{-1}(1/√2)+2cos^{-1}(√3/2)+cos^{-1}(0).
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Evaluate: 3π/4 + π/3 + π/2
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3 marks Medium answer
Evaluate: sec^2(tan^{-1}(1/2))+cot^2(cot^{-1}(1/3)).
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Evaluate: 5/4 + 10/9
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3 marks Medium answer
Evaluate: cot^2{cot^{-1}(−1/3)}+sin^2{cos^{-1}(1/3)}.
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Evaluate: 1/9 + 1/9
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3 marks Medium answer
Find the value of sin^2{cos^{-1}(3/5)}+tan^2{sec^{-1}(3)}.
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Evaluate: 16/25 + 9
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3 marks Medium answer
Find the value of tan^{-1}[2cos(2sin^{-1}(1/2))]+tan^{-1}(1).
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Evaluate: π/4 + π/4
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3 marks Medium answer
Find the value of tan^{-1}(−1/√3)+cot^{-1}(1/√3)+tan^{-1}[sin(−π/2)].
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Evaluate: −π/6 + π/6 + −π/2
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3 marks Medium answer
Find the value of sin^{-1}(−1/2)+cos^{-1}(−√3/2)+cot^{-1}(tan(4π/3)).
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Evaluate: −π/6 + 5π/6 + 4π/3
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3 marks Medium answer
Find the value of cos^{-1}(1/2)−tan^{-1}(−1/√3)+cot^{-1}(−2).
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Evaluate: π/3 + π/6 + π/3
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3 marks Medium answer
Find the value of tan^{-1}(tan(3π/5))+cos^{-1}(cos(13π/6))+sin^{-1}(−1/2).
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Evaluate: 3π/5 + 7π/6 + −π/6
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3 marks Medium answer
Find the value of k if sin^{-1}[k tan(2cos^{-1}(√3/2))]=π/3.
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k = 1/√3
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1 marks Short answer
Domain of sin^{-1}(2x−3) is
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(−√2,−1)∪(1,√2)
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1 marks Short answer
Domain of cos^{-1}(x)+sin^{-1}(x) is
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[−1,1]
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1 marks Short answer
If y=sin^{-1}(x),−1≤x≤0, then the range of y is
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[−π/2,0]
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1 marks Short answer
sin^{-1}(sqrt{3}/2) is equal to
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1/3
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1 marks Short answer
[sec^{-1}(−√2)−tan^{-1}(−1/√3)] is equal to
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5π/12
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1 marks Short answer
The principal value branch of cos^{-1}(x) is
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[0,π]
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1 marks Short answer
The principal value of sin^{-1}(cos(4π/5)) is
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3π/5
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1 marks Short answer
The principal value of sin^{-1}(sin(−10π/3)) is
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−π/3
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1 marks Short answer
The principal value of cot^{-1}(−1/√3) is
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−π/3
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1 marks Short answer
The value of cos(π/6+cot^{-1}(−√3)) is
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−√3/2
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1 marks Short answer
Assertion (A): Set of values of sec^{-1}(√3/2) is a null set. Reason (R): sec^{-1}(x) is defined for x∈R−(−1,1).
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Both assertion(A) and reason(R) are true and reason(R) is the correct explanation of assertion(A)
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1 marks Short answer
Assertion (A): The principal value of cot^{-1}(√3) is π/6. Reason (R): Domain of cot^{-1}(x) is ℝ−{−1,1}.
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Both assertion(A) and reason(R) are true and reason(R) is the correct explanation of assertion(A)
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