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Federal (FBISE) · Chapter test · Free

2nd Year Mathematics Chapter 8 Test08: Inverse Trigonometric Functions and Their Graphs

26 marks · 40 minutes · 17 questions. Covers: 08: Inverse Trigonometric Functions and Their Graphs.

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2nd Year Mathematics Chapter 8 Test

2nd Year · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 26Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 6 × 1 = 6)

  1. What results sec⁡−1(1)−sec⁡−1(2) \text{What results } \sec^{-1}(1) - \sec^{-1}(\sqrt{2})
    1. π6\frac{\pi}{6}
    2. π2\frac{\pi}{2}
    3. π3\frac{\pi}{3}
    4. π4\frac{\pi}{4}
  2. For what value of x ∈ (0 , 2π) , Sin x =−12-\frac{1}{2}
    1. 7π6,π6\frac{7\pi}{6}, \frac{\pi}{6}
    2. 7π6,11π6\frac{7\pi}{6}, \frac{11\pi}{6}
    3. 5π6,11π6\frac{5\pi}{6}, \frac{11\pi}{6}
    4. π6,5π6\frac{\pi}{6}, \frac{5\pi}{6}
  3. The value of cos⁡[π6+cos⁡−1(−12)] is : \text{The value of } \cos\left[\frac{\pi}{6} + \cos^{-1}\left(-\frac{1}{2}\right)\right] \text{ is :}
    1. 12\frac{1}{2}
    2. −12-\frac{1}{2}
    3. −32-\frac{\sqrt{3}}{2}
    4. 32\frac{\sqrt{3}}{2}
  4. , If sin⁡−1(12)=π2−x, then value of x is: \text{If } \sin^{-1} \left( \frac{1}{2} \right) = \frac{\pi}{2} - x \text{, then value of x is:} :
    1. π6\frac{\pi}{6}
    2. π3\frac{\pi}{3}
    3. π4\frac{\pi}{4}
    4. π2\frac{\pi}{2}
  5. If sin⁡−1(12)=π2−x, then what is the value of x? \text{If } \sin^{-1} \left( \frac{1}{2} \right) = \frac{\pi}{2} - x, \text{ then what is the value of } x?
    1. π2\frac{\pi}{2}
    2. π6\frac{\pi}{6}
    3. π4\frac{\pi}{4}
    4. π3\frac{\pi}{3}
  6. The value of Sin−1(513) is: \text{The value of } Sin^{-1} \left( \frac{5}{13} \right) \text{ is:}
    1. Tan−1(512)Tan^{-1} \left( \frac{5}{12} \right)
    2. cos(513)cos \left( \frac{5}{13} \right)
    3. cos−1(512)cos^{-1} \left( \frac{5}{12} \right)
    4. csc−1(1315)csc^{-1} \left( \frac{13}{15} \right)

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Draw the graph of each of the following functions against the intervals mentioned: y = sin⁻¹ (2x) for x ∈ [−12,12].\begin{bmatrix} -\frac{1}{2}, \frac{1}{2} \end{bmatrix}..
  2. Solve inverse trigonometric equation algebraically. 4 ArcTan² (x) - 3π ArcTan(x) - π² = 0
  3. Find the unknown angle and use a calculator to evaluate as real number to three decimal place.sin⁡−1(−15)=−cos⁡−1() \sin^{-1} \left( - \frac{1}{\sqrt{5}} \right) = - \cos^{-1} ( )
  4. Find the principal value of the following without using a calculator.r. cos⁡−1(32) \cos^{-1} \left( \frac{\sqrt{3}}{2} \right)
  5. Establish the identities. tan⁡−1(34)+Ttan⁡−1(17)=π4 \tan^{-1} \left( \frac{3}{4} \right) + T \tan^{-1} \left( \frac{1}{7} \right) = \frac{\pi}{4}
  6. Draw the graph of each of the following functions against the intervals mentioned: y = Tan⁡−¹(x²) for x ∈ ℝ
  7. Establish the identities.sin⁡−1(13)+sin⁡−1(223)=π2\sin^{-1}\left(\frac{1}{3}\right) + \sin^{-1}\left(\frac{2\sqrt{2}}{3}\right) = \frac{\pi}{2}
  8. Draw the graph of each of the following functions against the intervals mentioned: y = Cos−¹(2x − 1) for x ∈ [0 , 1]

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. Find the exact real number value of without using a calculator.sin⁡[sin⁡−123+cos⁡−112]\sin \left[ \sin^{-1} \frac{2}{3} + \cos^{-1} \frac{1}{2} \right]
  2. Draw the graph of the following functions and answer the questions given at the end. y=tan⁡−1(x−1)+π4for x∈R y = \tan^{-1} \left( x - 1 \right) +\frac{\pi}{4} \quad \text{for } x \in ℝ. Describe how the graph has been translated from the basic graph of y = Tan⁻¹ x.
  3. Find the exact real number value of without using a calculator.cos⁡−1(cos⁡π6) \cos^{-1} \left( \cos \frac{\pi}{6} \right)