Class 12 Inverse Trigonometric Functions worksheet

Sample questions

Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.

Section A · multiple choice

1. 1.

   The principal value of cos⁻¹(1/√2) is:

   1. π/4
   2. −π/4
   3. 3π/4
   4. π/6

   Answer

   (a) π/4

   the value must lie in the principal branch of cos⁻¹

2. 2.

   tan⁻¹(tan(4π/3)) equals:

   1. π/3
   2. 4π/3
   3. −π/3
   4. 2π/3

   Answer

   (a) π/3

   4π/3 is outside the principal branch; tan(4π/3) = tan(π/3) and π/3 lies in it

3. 3.

   cot(cos⁻¹(5/13)) equals:

   1. 5/12
   2. 12/5
   3. 12/13
   4. 5/13

   Answer

   (a) 5/12

   a right triangle with opposite side 12, adjacent side 5, hypotenuse 13

Section B · short answer

1. 4.

   Find the principal values of (a) sec⁻¹(2/√3), (b) sin⁻¹(1), (c) sin⁻¹(−1/√2).

   Answer

   (a) π/6; (b) π/2; (c) −π/4

   pick the angle in each principal branch

2. 5.

   Find the value of cos⁻¹(1/2) + sec⁻¹(−2) − sec⁻¹(−1).

   Answer

   0

   cos⁻¹(1/2) = π/3, sec⁻¹(−2) = 2π/3, sec⁻¹(−1) = π

Section C · long answer

1. 6.

   Find the principal values of cosec⁻¹(2/√3), cot⁻¹(√3), sec⁻¹(−1), and hence the value of their sum.

   Answer

   cosec⁻¹(2/√3) = π/3, cot⁻¹(√3) = π/6, sec⁻¹(−1) = π; sum = 3π/2

   each value from its principal branch

Fresh sheets for your child

In the app, every Inverse Trigonometric Functions sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.

Coming soon for Android and iPhone.

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