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 Inverse Trigonometric Functions 38 Flashcards |
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The inverse function of y = sin x is represented as ___ and defined for y in the interval ___ to ___. |
Card: 1 / 38 |
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Y = sin⁻¹ x, defined for y in the interval -π/2 to π/2. |
Card: 2 / 38 |
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True or False: The domain of cos⁻¹ x is limited to the interval [-1, 1]. |
Card: 3 / 38 |
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True. |
Card: 4 / 38 |
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Fill in the blanks: The relationship sin⁻¹(x) + cos⁻¹(x) = ___ is valid for all x in the interval ___ to ___. |
Card: 5 / 38 |
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Π/2; x in the interval [-1, 1]. |
Card: 6 / 38 |
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Domain of the function:
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Card: 7 / 38 |
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Card: 8 / 38 |
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Fill in the blank: The property tan⁻¹(-x) = ___ holds true for all x in _____. |
Card: 9 / 38 |
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-tan⁻¹(x); x in R. |
Card: 10 / 38 |
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If then x2+y2= ? |
Card: 11 / 38 |
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1 |
Card: 12 / 38 |
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True or False: The function sin⁻¹ x is multivalued over the interval [-1, 1]. |
Card: 13 / 38 |
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False; it has a unique principal value. |
Card: 14 / 38 |
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The relationship sin⁻¹(cos θ) = ___ is valid when θ is in the interval ___ to ___. |
Card: 15 / 38 |
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Π/2 - θ; θ in the interval [0, π]. |
Card: 16 / 38 |
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If y = cos⁻¹(-1/2), what is the value of y? |
Card: 17 / 38 |
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Y = 2π/3. |
Card: 18 / 38 |
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True or False: The inverse function tan⁻¹(x) + cot⁻¹(x) equals π/2 for all x in R. |
Card: 19 / 38 |
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True. |
Card: 20 / 38 |
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Fill in the blank: The property sec⁻¹(-x) = ___ for x in the interval |x| ≥ 1. |
Card: 21 / 38 |
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Π - sec⁻¹(x). |
Card: 22 / 38 |
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Fill in the blank: The property tan⁻¹(x) - tan⁻¹(y) = tan⁻¹[(x - y)/(1 + xy)] is valid when xy > ___. |
Card: 23 / 38 |
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-1. |
Card: 24 / 38 |
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If cos⁻¹(-x) = y, then the relationship can be expressed as ___ for x in the interval ___ to ___. |
Card: 25 / 38 |
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Y = π - cos⁻¹(x); x in the interval [-1, 1]. |
Card: 26 / 38 |
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Find: |
Card: 27 / 38 |
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Card: 28 / 38 |
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Which of the following is not correct about the graph of y = tan−1x? A) Increasing function |
Card: 29 / 38 |
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D) Even function (it’s odd) |
Card: 30 / 38 |
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What is the range of the function tan⁻¹ x? |
Card: 31 / 38 |
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The range of tan⁻¹ x is (-π/2, π/2). |
Card: 32 / 38 |
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Fill in the Blank: |
Card: 33 / 38 |
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Card: 34 / 38 |
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Which of the following is always true? A) sin−1(−x) = −sin−1x D) All of the above |
Card: 35 / 38 |
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D) All of the above |
Card: 36 / 38 |
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Evaluate:
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Card: 37 / 38 |
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π |
Card: 38 / 38 |
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Completed! Keep practicing to master all of them. |
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